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2005 Subcritical pseudodifferential equation on a half-line with nonanalytic symbol
Elena I. Kaikina
Differential Integral Equations 18(12): 1341-1370 (2005).

Abstract

We study nonlinear pseudodifferential equations on a half-line with a nonanalytic symbol \begin{equation*} \left\{ \begin{array}{c} \partial _{t}u+\mathbb{K}u=\lambda \left\vert u\right\vert ^{\sigma }u,\text{ }x\in \mathbf{R}^{+},\text{ }t>0, \\ u\left( 0,x\right) =u_{0}\left( x\right) \text{, }x\in \mathbf{R}^{+}, \end{array} \right. \end{equation*} where $0<$ $\sigma <1,$ $\lambda \in \mathbf{R}$ and \begin{equation*} \mathbb{K}u=\frac{1}{2\pi i}\theta (x)\int_{-i\infty }^{i\infty }e^{px}K(p) \widehat{u}(t,p)dp,\qquad K(p)=\frac{p^{2}}{p^{2}-1}. \end{equation*} The aim of this paper is to prove the global existence of solutions to the initial-boundary-value problem and to find the main term of the asymptotic representation of solutions in subcritical case, when the nonlinear term of equation has the time decay rate less than that of the linear terms.

Citation

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Elena I. Kaikina. "Subcritical pseudodifferential equation on a half-line with nonanalytic symbol." Differential Integral Equations 18 (12) 1341 - 1370, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35524
MathSciNet: MR2174976

Subjects:
Primary: 35S15
Secondary: 35B40 , 35C20

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 12 • 2005
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