Journal of Integral Equations and Applications Articles (Project Euclid)
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The latest articles from Journal of Integral Equations and Applications on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 22 Mar 2011 10:06 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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The determination of boundary coefficients from far field measurements
http://projecteuclid.org/euclid.jiea/1277125620
<strong>Fioralba Cakoni</strong>, <strong>David Colton</strong>, <strong>Peter Monk</strong><p><strong>Source: </strong>J. Integral Equations Appl., Volume 22, Number 2, 167--191.</p>projecteuclid.org/euclid.jiea/1277125620_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTSuperconvergent Projection Methods for Hammerstein Integral Equationshttps://projecteuclid.org/euclid.jiea/1497686428<strong> Allouch, Sbibih, Tahrichi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1497686428_20180405220043Thu, 05 Apr 2018 22:00 EDTUniform Exponential Stability and Its Applications to Bounded Solutions of Integro-Differential Equations in Banach Spaceshttps://projecteuclid.org/euclid.jiea/1497686431<strong> Chang, Ponce</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1497686431_20180405220043Thu, 05 Apr 2018 22:00 EDTIterative Methods for a Fractional Order Volterra Population Modelhttps://projecteuclid.org/euclid.jiea/1522980020<strong> Roy, Vijesh, Chandhini</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980020_20180405220043Thu, 05 Apr 2018 22:00 EDTSolvability of Linear Boundary Value Problems for Subdiffusuion Equations with Memoryhttps://projecteuclid.org/euclid.jiea/1502676034<strong> Krasnoschok, Pata, Vasylyeva</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1502676034_20180405220043Thu, 05 Apr 2018 22:00 EDTNumerical Solutions of a Class of Singular Neutral Functional Differential Equations on Graded Mesheshttps://projecteuclid.org/euclid.jiea/1503129642<strong> Perez-Nagera, Turi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1503129642_20180405220043Thu, 05 Apr 2018 22:00 EDTEnergy Decay Rates for the Solutions of the Kirchhoff Type Wave Equation with Boundary Damping and Source Termshttps://projecteuclid.org/euclid.jiea/1510304523<strong> Ha</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304523_20180405220043Thu, 05 Apr 2018 22:00 EDTRegularity Properties of Mild Solutions for a Class of Volterra Equationshttps://projecteuclid.org/euclid.jiea/1490583517<strong> Abadias, Alvarez, Lizama</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1490583517_20180405220043Thu, 05 Apr 2018 22:00 EDTOn a Bohr-Neugebauer Property for Some Almost Automorphic Abstract Delay Equationshttps://projecteuclid.org/euclid.jiea/1505376021<strong> Benkhalti, Es-sebbar, Ezzinbi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1505376021_20180405220043Thu, 05 Apr 2018 22:00 EDTExponential Decay Estimates of the Eigenvalues for the Neumann-Poincare Operator on Analytic Boundaries in two Dimensionshttps://projecteuclid.org/euclid.jiea/1510304520<strong> Ando, Kang, Miyanishi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304520_20180405220043Thu, 05 Apr 2018 22:00 EDTOn Some Classes of Elliptic Systems with Fractional Boundary Relaxationhttps://projecteuclid.org/euclid.jiea/1502676035<strong> Pruss</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1502676035_20180405220043Thu, 05 Apr 2018 22:00 EDTInverse Scattering for Shape and Impedance Revisitedhttps://projecteuclid.org/euclid.jiea/1505376023<strong> Kress, Rundell</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1505376023_20180405220043Thu, 05 Apr 2018 22:00 EDTOn the Unique Characterization of Continuous Distributions by Single Regression of Non-Adjacent Generalized Order Statisticshttps://projecteuclid.org/euclid.jiea/1522980027<strong> Bieniek, Maciag</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980027_20180405220043Thu, 05 Apr 2018 22:00 EDTA Note on the Well-Posedness of Terminal Value Problems for Fractional Differential Equationshttps://projecteuclid.org/euclid.jiea/1497686433<strong> Diethelm, Ford</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1497686433_20180405220043Thu, 05 Apr 2018 22:00 EDTEssential Norm of Generalized Weighted Composition Operators from $H^{\infty}$ to the Logarithmic Bloch Spacehttps://projecteuclid.org/euclid.jiea/1510304525<strong> Zhang</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304525_20180405220043Thu, 05 Apr 2018 22:00 EDTExtrapolation Methods for the Numerical Solution of Nonlinear Fredholm Integer Equatonshttps://projecteuclid.org/euclid.jiea/1510304521<strong> Brezinski, Redivo-Zaglia</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304521_20180405220043Thu, 05 Apr 2018 22:00 EDTL^{p} Bounds for a Class of Marcinkiewicz Internal Operatorshttps://projecteuclid.org/euclid.jiea/1522980028<strong> Al-Salman</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980028_20180405220043Thu, 05 Apr 2018 22:00 EDTOn the Numerical Solution of the Exterior Elastodynamic Problem by a Boundary Integral Equation Methodhttps://projecteuclid.org/euclid.jiea/1505376022<strong> Chapko, Mindrinos</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1505376022_20180405220043Thu, 05 Apr 2018 22:00 EDTStable and Center Stable Manifolds of Admissible Classes for Partial Functional Differential Equationshttps://projecteuclid.org/euclid.jiea/1510304522<strong> Duoc, Huy</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304522_20180405220043Thu, 05 Apr 2018 22:00 EDTA Hybrid Collocation Method for Fractional Initial Value Problemshttps://projecteuclid.org/euclid.jiea/1522980029<strong> Wang, Wang, Cao</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980029_20180405220043Thu, 05 Apr 2018 22:00 EDTFractional Differential Systems with Applications to a Stability Analyseshttps://projecteuclid.org/euclid.jiea/1522980030<strong> Gallegos, Duarte-Mermoud. Aguia-Camacho</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980030_20180405220043Thu, 05 Apr 2018 22:00 EDTOn the Oscillation of Discrete Volterra Equations with Positive and Negative Nonlinearitieshttps://projecteuclid.org/euclid.jiea/1510304524<strong> Ozbekler</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1510304524_20180405220043Thu, 05 Apr 2018 22:00 EDTFractional Diffusion Equation with the Distributed Order Caputo Derivativehttps://projecteuclid.org/euclid.jiea/1522980031<strong> Kubica, Ryszewska</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Forthcoming articles, --.</p>projecteuclid.org/euclid.jiea/1522980031_20180405220043Thu, 05 Apr 2018 22:00 EDTIntroduction to the Special Issue honoring W.E.~Olmsteadhttps://projecteuclid.org/euclid.jiea/1523347334<strong>Colleen M. Kirk</strong>, <strong>Catherine A. Roberts</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 1--1.</p>projecteuclid.org/euclid.jiea/1523347334_20180410040232Tue, 10 Apr 2018 04:02 EDTOn the contributions of W. Edward Olmsteadhttps://projecteuclid.org/euclid.jiea/1523347335<strong>C.M. Kirk</strong>, <strong>L.R. Ritter</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 3--15.</p><p><strong>Abstract:</strong><br/>
With this article, we wish to honor the many contributions of our mentor, colleague and dear friend, Professor W.~Edward Olmstead, on the occasion of his retirement from Northwestern University. Ed has spent over five decades at Northwestern University, first as a graduate student and then as a member of the faculty. During this time he completed his PhD, played a key role in the formation of the Department of Engineering Science and Applied Mathematics (ESAM), developed several courses in applied mathematics, participated in the education of numerous students, and made vast and important contributions in the field of applied mathematics. Here, we give a (mostly chronological) account of some of Ed's major research interests and contributions, primarily in the field of Integral Equations.
</p>projecteuclid.org/euclid.jiea/1523347335_20180410040232Tue, 10 Apr 2018 04:02 EDTOn a semi-linear system of nonlocal time and space reaction diffusion equations with exponential nonlinearitieshttps://projecteuclid.org/euclid.jiea/1523347336<strong>B. Ahmad</strong>, <strong>A. Alsaedi</strong>, <strong>D. Hnaien</strong>, <strong>M. Kirane</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 17--40.</p><p><strong>Abstract:</strong><br/>
In this article, we investigate the local existence of a unique mild solution to a reaction diffusion system with time-nonlocal nonlinearities of exponential growth. Moreover, blowing-up solutions are shown to exist, and their time blow-up profile is presented.
</p>projecteuclid.org/euclid.jiea/1523347336_20180410040232Tue, 10 Apr 2018 04:02 EDTExistence of a solution for the problem with a concentrated source in a subdiffusive mediumhttps://projecteuclid.org/euclid.jiea/1523347337<strong>C.Y. Chan</strong>, <strong>H.T. Liu</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 41--65.</p><p><strong>Abstract:</strong><br/>
By using Green's function, the problem is converted into an integral equation. It is shown that there exists a $t_b$ such that, for $0\leq t\lt t_b$, the integral equation has a unique nonnegative continuous solution $u$; if $t_b$ is finite, then $u$ is unbounded in $[0, t_b)$. Then, $u$ is proved to be the solution of the original problem.
</p>projecteuclid.org/euclid.jiea/1523347337_20180410040232Tue, 10 Apr 2018 04:02 EDTBlow-up of solutions for semilinear fractional Schrödinger equationshttps://projecteuclid.org/euclid.jiea/1523347338<strong>A.Z. Fino</strong>, <strong>I. Dannawi</strong>, <strong>M. Kirane</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 67--80.</p><p><strong>Abstract:</strong><br/>
We consider the Cauchy problem in $\mathbb {R}^N$, $N \geq 1$, for the semi-linear Schr\"odinger equation with fractional Laplacian. We present the local well-posedness of solutions in $H^{{\alpha }/{2}}(\mathbb {R}^N)$, $0\lt \alpha \lt 2$. We prove a finite-time blow-up result, under suitable conditions on the initial data.
</p>projecteuclid.org/euclid.jiea/1523347338_20180410040232Tue, 10 Apr 2018 04:02 EDTA blow-up result to a delayed Cauchy viscoelastic problemhttps://projecteuclid.org/euclid.jiea/1523347339<strong>Mohammad Kafini</strong>, <strong>Muhammad I. Mustafa</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 81--94.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a Cauchy problem for a nonlinear viscoelastic equation with delay. Under suitable conditions on the initial data and the relaxation function, in the whole space, we prove a finite-time blow-up result.
</p>projecteuclid.org/euclid.jiea/1523347339_20180410040232Tue, 10 Apr 2018 04:02 EDTGeneral decay for a laminated beam with structural damping and memory: The case of non-equal wave speedshttps://projecteuclid.org/euclid.jiea/1523347340<strong>Gang Li</strong>, <strong>Xiangyu Kong</strong>, <strong>Wenjun Liu</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 95--116.</p><p><strong>Abstract:</strong><br/>
In previous work, Lo and Tatar studied the exponential decay for a laminated beam with viscoelastic damping acting on the effective rotation angle in the case of equal-speed wave propagations. In this paper, we continue consideration of the same problem in the case of non-equal wave speeds. In this case, the main difficulty is how to estimate the non-equal speed term. To overcome this difficulty, the second-order energy method introduced in Guesmia and Messaoudi seems to be the best choice for our problem. For a wide class of relaxation functions, we establish the general decay result for the energy without any kind of internal or boundary control.
</p>projecteuclid.org/euclid.jiea/1523347340_20180410040232Tue, 10 Apr 2018 04:02 EDTGeneral and optimal decay in a memory-type Timoshenko systemhttps://projecteuclid.org/euclid.jiea/1523347341<strong>Salim A. Messaoudi</strong>, <strong>Jamilu Hashim Hassan</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 117--145.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with the following memory-type Timoshenko system \[ \rho _1\varphi _{tt}-K(\varphi _x+\psi )_x=0 \] \[ \rho _2\psi _{tt}-b\psi _{xx}+K(\varphi _x+\psi )+ \displaystyle \int _0^tg(t-s)\psi _{xx}(s)\,ds=0, \] $(x,t)\in (0,L)\times (0,\infty )$, with Dirichlet boundary conditions, where $g$ is a positive non-increasing function satisfying, for some constant $1\leq p\lt {3}/{2}$, \[ g'(t)\leq -\xi (t)g^p(t),\quad \mbox {for all }t\geq 0. \] We prove some decay results which generalize and improve many earlier results in the literature. In particular, our result gives the optimal decay for the case of polynomial stability.
</p>projecteuclid.org/euclid.jiea/1523347341_20180410040232Tue, 10 Apr 2018 04:02 EDTCoupled Volterra integral equations with blowing up solutionshttps://projecteuclid.org/euclid.jiea/1523347342<strong>Wojciech Mydlarczyk</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 147--166.</p><p><strong>Abstract:</strong><br/>
In this paper, a system of nonlinear integral equations related to combustion problems is considered. Necessary and sufficient conditions for the existence and explosion of positive solutions are given. In addition, the uniqueness of the positive solutions is shown. The main results are obtained by monotonicity methods.
</p>projecteuclid.org/euclid.jiea/1523347342_20180410040232Tue, 10 Apr 2018 04:02 EDTSolution estimates for a system of nonlinear integral equations arising in optometryhttps://projecteuclid.org/euclid.jiea/1523347343<strong>Wojciech Okrasiński</strong>, <strong>Łukasz Płociniczak</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 167--179.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate a system of nonlinear integral equations that has previously been proposed in modelling of the human cornea. The main result of our work is a construction of lower and upper estimates that bound the components of the exact solution to the system being considered. These results generalize some of the recent work by other authors. We conclude the paper with a numerical verification of our analytical estimates.
</p>projecteuclid.org/euclid.jiea/1523347343_20180410040232Tue, 10 Apr 2018 04:02 EDTBlow up of fractional reaction-diffusion systems with and without convection termshttps://projecteuclid.org/euclid.jiea/1523347344<strong>Aroldo Pérez</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 181--196.</p><p><strong>Abstract:</strong><br/>
Based on the study of blow up of a particular system of ordinary differential equations, we give a sufficient condition for blow up of positive mild solutions to the Cauchy problem of a fractional reaction-diffusion system, and, by a comparison between the transition densities of the semigroups generated by $\Delta _\alpha :=-(-\Delta )^{\alpha /2}$ and $\Delta _\alpha +b(x)\cdot \nabla $ for $1\lt \alpha \lt 2$, $d\geq 1$ and $b$ in the Kato class on $\mathbb {R}^d$, we prove that this condition is also sufficient for the blow up of a fractional diffusion-convection-reaction system.
</p>projecteuclid.org/euclid.jiea/1523347344_20180410040232Tue, 10 Apr 2018 04:02 EDTSplit-step collocation methods for stochastic Volterra integral equationshttps://projecteuclid.org/euclid.jiea/1523347345<strong>Y. Xiao</strong>, <strong>J.N. Shi</strong>, <strong>Z.W. Yang</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 1, 197--218.</p><p><strong>Abstract:</strong><br/>
In this paper, a split-step collocation method is proposed for solving linear stochastic Volterra integral equations (SVIEs) with smooth kernels. The H\"older condition and the conditional expectations of the exact solutions are investigated. The solvability and mean-square boundedness of numerical solutions are proved and the strong convergence orders of collocation solutions and iterated collocation solutions are also shown. In addition, numerical experiments are provided to verify the conclusions.
</p>projecteuclid.org/euclid.jiea/1523347345_20180410040232Tue, 10 Apr 2018 04:02 EDTRegularity properties of mild solutions for a class of Volterra equations with critical nonlinearitieshttps://projecteuclid.org/euclid.jiea/1536804117<strong>Luciano Abadias</strong>, <strong>Edgardo Alvarez</strong>, <strong>Carlos Lizama</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 2, 219--256.</p><p><strong>Abstract:</strong><br/>
We study a class of abstract nonlinear integral equations of convolution type defined on a Banach space. We prove the existence of a unique, locally mild solution and an extension property when the nonlinear term satisfies a local Lipschitz condition. Moreover, we guarantee the existence of the global mild solution and blow up profiles for a large class of kernels and nonlinearities. If the nonlinearity has critical growth, we prove the existence of the local $\epsilon $-mild solution. Our results improve and extend recent results for special classes of kernels corresponding to nonlocal in time equations. We give an example to illustrate the application of the theorems so obtained.
</p>projecteuclid.org/euclid.jiea/1536804117_20180912220202Wed, 12 Sep 2018 22:02 EDTExistence of a mild solution for a neutral stochastic fractional integro-differential inclusion with a nonlocal conditionhttps://projecteuclid.org/euclid.jiea/1536804118<strong>Alka Chadha</strong>, <strong>D. Bahuguna</strong>, <strong>Dwijendra N. Pandey</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 2, 257--291.</p><p><strong>Abstract:</strong><br/>
This paper mainly concerns the existence of a mild solution for a neutral stochastic fractional integro-differential inclusion of order $1\lt \beta \lt 2$ with a nonlocal con\-dition in a separable Hilbert space. Utilizing the fixed point theorem for multi-valued operators due to O' Regan, we establish an existence result involving a $\beta $-resolvent operator. An illustrative example is provided to show the effectiveness of the established results.
</p>projecteuclid.org/euclid.jiea/1536804118_20180912220202Wed, 12 Sep 2018 22:02 EDTInverse scattering for shape and impedance revisitedhttps://projecteuclid.org/euclid.jiea/1536804119<strong>Rainer Kress</strong>, <strong>William Rundell</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 2, 293--311.</p><p><strong>Abstract:</strong><br/>
The inverse scattering problem under consideration is to reconstruct both the shape and the impedance function of an impenetrable two-dimensional obstacle from the far field pattern for scattering of time-harmonic acoustic or E-polarized electromagnetic plane waves. We propose an inverse algorithm that is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. This extends the approach we suggested for an inverse boundary value problem for harmonic functions in Kress and Rundell(2005) and is a counterpart of our earlier work on inverse scattering for shape and impedance in Kress and Rundell(2001). We present the mathematical foundation of the method and exhibit its feasibility by numerical examples.
</p>projecteuclid.org/euclid.jiea/1536804119_20180912220202Wed, 12 Sep 2018 22:02 EDTOn a Bohr-Neugebauer property for some almost automorphic abstract delay equationshttps://projecteuclid.org/euclid.jiea/1541668116<strong>Rachid Benkhalti</strong>, <strong>Brahim Es-sebbar</strong>, <strong>Khalil Ezzinbi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 313--345.</p><p><strong>Abstract:</strong><br/>
This paper is a continuation of the investigations done in the literature regarding the so called Bohr-Neugebauer property for almost periodic differential equations in Hilbert spaces. The aim of this work is to extend the investigation of this property to almost automorphic functional partial differential equations in Banach spaces. We use a compactness assumption which turns out to relax assumptions made in some earlier works for differential equations in Hilbert spaces. Two new integration theorems for almost automorphic functions are proven in the process. To illustrate our main results, we propose an application to a reaction-diffusion equation with continuous delay.
</p>projecteuclid.org/euclid.jiea/1541668116_20181108040841Thu, 08 Nov 2018 04:08 ESTUniform exponential stability and applications to bounded solutions of integro-differential equations in Banach spaceshttps://projecteuclid.org/euclid.jiea/1541668117<strong>Yong-Kui Chang</strong>, <strong>Rodrigo Ponce</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 347--369.</p><p><strong>Abstract:</strong><br/>
Let $\mathbb {X}$ be a Banach space. Let $A$ be the generator of an immediately norm continuous $C_0$-semigroup defined on $\mathbb {X}$. We study the uniform exponential stability of solutions of the Volterra equation
$u'(t) = Au(t)+\displaystyle \int _0^t a(t-s)Au(s)\,ds,\quad t\geq 0,\ u(0)=x$,
\noindent where $a$ is a suitable kernel and $x\in \mathbb {X}$. Using a matrix operator, we obtain some spectral conditions on $A$ that ensure the existence of constants $C,\omega >0$ such that $\|u(t)\|\leq Ce^{-\omega t}\|x\|$, for each $x\in D(A)$ and all $t\geq 0$. With these results, we prove the existence of a uniformly exponential stable resolvent family to an integro-differential equation with infinite delay. Finally, sufficient conditions are established for the existence and uniqueness of bounded mild solutions to this equation.
</p>projecteuclid.org/euclid.jiea/1541668117_20181108040841Thu, 08 Nov 2018 04:08 ESTA note on the well-posedness of terminal value problems for fractional differential equationshttps://projecteuclid.org/euclid.jiea/1541668118<strong>Kai Diethelm</strong>, <strong>Neville J. Ford</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 371--376.</p><p><strong>Abstract:</strong><br/>
This note is intended to clarify some important points about the well-posedness of terminal value problems for fractional differential equations. It follows the recent publication of a paper by Cong and Tuan in this journal, in which a counter-example calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights, that a wide class of terminal value problems of fractional differential equations is well posed, and we identify those cases where the well-posedness question must be regarded as open.
</p>projecteuclid.org/euclid.jiea/1541668118_20181108040841Thu, 08 Nov 2018 04:08 ESTEnergy decay rates for solutions of the Kirchhoff type wave equation with boundary damping and source termshttps://projecteuclid.org/euclid.jiea/1541668119<strong>Tae Gab Ha</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 377--415.</p><p><strong>Abstract:</strong><br/>
In this work, we are concerned with uniform stabilization for an initial-boundary value problem associated with the Kirchhoff type wave equation with feedback terms and memory condition at the boundary. We prove that the energy decays exponentially when the boundary damping term has a linear growth near zero and polynomially when the boundary damping term has a polynomial growth near zero. Furthermore, we study the decay rate of the energy without imposing any restrictive growth assumption on the damping term near zero.
</p>projecteuclid.org/euclid.jiea/1541668119_20181108040841Thu, 08 Nov 2018 04:08 ESTSolvability of linear boundary value problems for subdiffusion equations with memoryhttps://projecteuclid.org/euclid.jiea/1541668120<strong>Mykola Krasnoschok</strong>, <strong>Vittorino Pata</strong>, <strong>Nataliya Vasylyeva</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 417--445.</p><p><strong>Abstract:</strong><br/>
For $\nu \in (0,1)$, the nonautonomous integro-differential equation \[ \mathbf {D}_{t}^{\nu }u-\mathcal {L}_{1}u-\int _{0}^{t}\mathcal {K}_{1}(t-s)\mathcal {L}_{2}u(\cdot ,s)\,ds =f(x,t) \] is considered here, where $\mathbf {D}_{t}^{\nu }$ is the Caputo fractional derivative and $\mathcal {L}_{1}$ and $\mathcal {L}_{2}$ are uniformly elliptic operators with smooth coefficients dependent on time. The global classical solvability of the associated initial-boundary value problems is addressed.
</p>projecteuclid.org/euclid.jiea/1541668120_20181108040841Thu, 08 Nov 2018 04:08 ESTNumerical solutions of a class of singular neutral functional differential equations on graded mesheshttps://projecteuclid.org/euclid.jiea/1541668121<strong>Pedro Perez-Nagera</strong>, <strong>Janos Turi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 3, 447--472.</p><p><strong>Abstract:</strong><br/>
In this paper, we present case studies to illustrate the dependence of the rate of convergence of numerical schemes for singular neutral equations (SNFDEs) on the particular mesh employed in the computation. In Ito and Turi, a semigroup theoretical framework was used to show convergence of semi- and fully- discrete methods for a class of SNFDEs with weakly singular kernels. On the other hand, numerical experiments in Ito and Turi demonstrated a ``degradation" of the expected rate of convergence when uniform meshes were considered. In particular, it was numerically observed that the degradation of the rate of convergence was related to the strength of the singularity in the kernel of the SNFDE. Following the idea used for Volterra equations with weakly singular kernels, see, e.g., Brunner, we investigate graded meshes associated with the kernel of the SNFDE in attempting to restore convergence rates.
</p>projecteuclid.org/euclid.jiea/1541668121_20181108040841Thu, 08 Nov 2018 04:08 ESTExponential decay estimates of the eigenvalues for the Neumann-Poincare operator on analytic boundaries in two dimensionshttps://projecteuclid.org/euclid.jiea/1543482173<strong>Kazunori Ando</strong>, <strong>Hyeonbae Kang</strong>, <strong>Yoshihisa Miyanishi</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 473--489.</p><p><strong>Abstract:</strong><br/>
We show that the eigenvalues of the Neumann-Poincare operator on analytic boundaries of simply connected bounded planar domains tend to zero exponentially fast, and the exponential convergence rate is determined by the maximal Grauert radius of the boundary. We present a few examples of boundaries to show that the estimate is optimal.
</p>projecteuclid.org/euclid.jiea/1543482173_20181129040258Thu, 29 Nov 2018 04:02 ESTOn the unique characterization of continuous distributions by single regression of non-adjacent generalized order statisticshttps://projecteuclid.org/euclid.jiea/1543482174<strong>Mariusz Bieniek</strong>, <strong>Krystyna Maciag</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 491--519.</p><p><strong>Abstract:</strong><br/>
We show a new and unexpected application of integral equations and their systems to the problem of the unique identification of continuous probability distributions based on the knowledge of exactly one regression function of ordered statistical data. The most popular example of such data are the order statistics which are obtained by non-decreasing ordering of elements of the sample according to their magnitude. However, our considerations are conducted in the abstract setting of so-called generalized order statistics. This model includes order statistics and other interesting models of ordered random variables. We prove that the uniqueness of characterization is equivalent to the uniqueness of the solution to the appropriate system of integral equations with non-classical initial conditions. This criterion for uniqueness is then applied to give new examples of characterizations.
</p>projecteuclid.org/euclid.jiea/1543482174_20181129040258Thu, 29 Nov 2018 04:02 ESTOn the numerical solution of the exterior elastodynamic problem by a boundary integral equation methodhttps://projecteuclid.org/euclid.jiea/1543482175<strong>Roman Chapko</strong>, <strong>Leonidas Mindrinos</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 521--542.</p><p><strong>Abstract:</strong><br/>
A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth, closed, simply connected two-dimensional domain, is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and a boundary integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the time-dependent problem to a sequence of stationary boundary value problems, which are solved by a boundary layer approach resulting in a sequence of boundary integral equations of the first kind. The numerical discretization and solution are obtained by a trigonometrical quadrature method. Numerical results are included.
</p>projecteuclid.org/euclid.jiea/1543482175_20181129040258Thu, 29 Nov 2018 04:02 ESTStable and center-stable manifolds of admissible classes for partial functional differential equationshttps://projecteuclid.org/euclid.jiea/1543482176<strong>Trinh Viet Duoc</strong>, <strong>Nguyen Thieu Huy</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 543--575.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the existence of stable and center-stable manifolds of admissible classes for mild solutions to partial functional differential equations of the form $\dot {u}(t)=A(t)u(t)+f(t,u_t)$, $t\ge 0$. These manifolds are constituted by trajectories of the solutions belonging to admissible function spaces which contain wide classes of function spaces like $L_p$-spaces and many other function spaces occurring in interpolation theory such as the Lorentz spaces $L_{p,q}$. Results in this paper are the generalization and development for our results in \cite {HD1}. The existence of these manifolds obtained in the case that the family of operators $(A(t))_{t\ge 0}$ generate the evolution family $(U(t,s))_{t\ge s\ge 0}$ having an exponential dichotomy or trichotomy on the half-line and the nonlinear forcing term $f$ satisfies the $\varphi $-Lipschitz condition, i.e., $\| f(t,u_t) -f(t,v_t)\| \le \varphi (t)\|u_t -v_t\|_{\mathcal {C}}$, where $u_t,\ v_t \in \mathcal{C} :=C([-r, 0], X)$, and $\varphi (t)$ belongs to some admissible Banach function space and satisfies certain conditions.
</p>projecteuclid.org/euclid.jiea/1543482176_20181129040258Thu, 29 Nov 2018 04:02 ESTOn the oscillation of discrete Volterra equations with positive and negative nonlinearitieshttps://projecteuclid.org/euclid.jiea/1543482177<strong>Abdullah Ozbekler</strong>. <p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 577--591.</p><p><strong>Abstract:</strong><br/>
In this paper, we give new oscillation criteria for discrete Volterra equations having different non-linearities such as super-linear and sub-linear cases. We also present some new sufficient conditions for oscillation under the effect of the oscillatory forcing term.
</p>projecteuclid.org/euclid.jiea/1543482177_20181129040258Thu, 29 Nov 2018 04:02 ESTVolume Index to Volume 30 (2018)https://projecteuclid.org/euclid.jiea/1544207666<p><strong>Source: </strong>Journal of Integral Equations and Applications, Volume 30, Number 4, 593--594.</p>projecteuclid.org/euclid.jiea/1544207666_20181207133438Fri, 07 Dec 2018 13:34 EST