Energy decay and nonexistence of solution for a reaction-diffusion equation with exponential nonlinearity
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
Boundary Value Problems 2014, 2014:70 doi:10.1186/1687-2770-2014-70Published: 25 March 2014
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.