Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

Abstract

The blow-up problems of the solution are considered for a reaction-diffusion equation with nonlocal source and variable exponent. Firstly, the local existence and uniqueness of solutions to problem is proved under the help of the fixed point theorem. Secondly, by using the super- and sub-solution method, we determine some sufficient conditions for the occurrence of finite time blow-up under the homogeneous Dirichlet boundary conditions, i.e. the variable exponent is positive and the initial data is large enough. Moreover, the estimates of upper and lower bounds of blow-up time are given.