Translator Disclaimer
July/August 2012 Global existence and blow up results for a heat equation with nonlinear nonlocal term
Miguel Loayza
Differential Integral Equations 25(7/8): 665-683 (July/August 2012).

Abstract

We study the nonlocal parabolic equation $$ u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s) \, ds $$ with $p>1$. We assume that $k$ is continuous and there exists $\gamma \in {\mathbb{R}}$ such that $k(\lambda t, \lambda s)=\lambda^{-\gamma}k(t,s)$ for all $\lambda>0$, $0<s<t$. We consider the problem in ${\mathbb{R}}^N$ and a Dirichlet problem in a bounded smooth domain $\Omega$. We analyze the conditions for either blow up or global existence of solutions.

Citation

Download Citation

Miguel Loayza. "Global existence and blow up results for a heat equation with nonlinear nonlocal term." Differential Integral Equations 25 (7/8) 665 - 683, July/August 2012.

Information

Published: July/August 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1265.35122
MathSciNet: MR2975689

Subjects:
Primary: 35B33, 35B44, 35K154

Rights: Copyright © 2012 Khayyam Publishing, Inc.

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.25 • No. 7/8 • July/August 2012
Back to Top