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Open Access Research

Energy decay and nonexistence of solution for a reaction-diffusion equation with exponential nonlinearity

Huiya Dai12* and Hongwei Zhang2

Author Affiliations

1 School of Mathematics and Statistics, Xi’an Jiaotong University, Xianning Road, Xi’an, P.R. China

2 Department of Mathematics, Henan University of Technology, Lianhua Street, Zhengzhou, P.R. China

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Boundary Value Problems 2014, 2014:70  doi:10.1186/1687-2770-2014-70

Published: 25 March 2014

Abstract

In this work we consider the energy decay result and nonexistence of global solution for a reaction-diffusion equation with generalized Lewis function and nonlinear exponential growth. There are very few works on the reaction-diffusion equation with exponential growth f as a reaction term by potential well theory. The ingredients used are essentially the Trudinger-Moser inequality.

Keywords:
reaction-diffusion equation; stable and unstable set; exponential reaction term; decay rate; global nonexistence