Differential and Integral Equations

Self-similar solutions, uniqueness and long-time asymptotic behavior for semilinear heat equations

Lucas Catão de Freitas Ferreira and Elder Jesús Villamizar-Roa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We analyze the well-posedness of the initial-value problem for the semilinear equation in Marcinkiewicz spaces $L^{(p,\infty)}$. Mild solutions are obtained in spaces with the right homogeneity to allow the existence of self-similar solutions. As a consequence of our results we prove that the class $C([0,T);L^{p}(\Omega)),\ 0 < T\leq\infty, \ p={\frac{n(\rho-1)}{2\gamma }},$ $\Omega=R^{n},$ has uniqueness of solutions (including large solutions) obtained in [19], [20] and [8]. The asymptotic stability of solutions is obtained, and as a consequence, a criterion for self-similarity persistence at large times is obtained.

Article information

Source
Differential Integral Equations, Volume 19, Number 12 (2006), 1349-1370.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050293

Mathematical Reviews number (MathSciNet)
MR2279332

Zentralblatt MATH identifier
1212.35205

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B40: Asymptotic behavior of solutions 35C05: Solutions in closed form 35K15: Initial value problems for second-order parabolic equations

Citation

Ferreira, Lucas Catão de Freitas; Villamizar-Roa, Elder Jesús. Self-similar solutions, uniqueness and long-time asymptotic behavior for semilinear heat equations. Differential Integral Equations 19 (2006), no. 12, 1349--1370. https://projecteuclid.org/euclid.die/1356050293


Export citation