Differential and Integral Equations

Blow-up behavior for semilinear heat equations in nonconvex domains

Chi-Cheung Poon

Abstract

We study solutions of the parabolic equation $u_t = \Delta u + u^p$. We wish to extend some results of Giga and Kohn to the situations where the solution, $u$, is defined on a $C^{2,\alpha}$ domain and satisfies the Dirichlet or the Neumann boundary condition.

Article information

Source
Differential Integral Equations, Volume 13, Number 7-9 (2000), 1111-1138.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356061213

Mathematical Reviews number (MathSciNet)
MR1775249

Zentralblatt MATH identifier
0990.35022

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Poon, Chi-Cheung. Blow-up behavior for semilinear heat equations in nonconvex domains. Differential Integral Equations 13 (2000), no. 7-9, 1111--1138. https://projecteuclid.org/euclid.die/1356061213