Global and blow‐up analysis for a class of nonlinear reaction diffusion model with Dirichlet boundary conditions

Abstract

The work is concerned with the following nonlinear reaction diffusion model with Dirichlet boundary conditions: urn:x-wiley:mma:media:mma5241:mma5241-math-0001 where p ≥ 2 is a real number and is a bounded domain with smooth boundary ∂D. Under some appropriate assumptions on the functions f,h,k,g,ρ, and initial value u0, by defining auxiliary functions and using a first‐order differential inequality technique, we not only present that the solution exists globally or blows up in a finite time but also compute the upper and lower bound for blow‐up time when blow‐up occurs. Additionally, two examples are given to illustrate the main results.