Blow-up time analysis of parabolic equations with variable nonlinearities

The blow-up of a class of nondegenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient a(x, t) allowed us to discuss our blow-up results differently. We prove blow-up results and give a new lower and upper bounds of the blow-up time to a class of semilinear reaction-diffusion equations and a nonlinear equation governed by them (x, t)-Laplacian, form (x, t) > 1.

Automated summary

This paper investigates the blow-up problem of a class of nondegenerate parabolic equations in a bounded domain. By discussing the nonnegative diffusion coefficient, we prove the blow-up results and provide new lower and upper bounds for the blow-up time of a class of semilinear reaction-diffusion equations and a nonlinear equation governed by (x, t)-Laplacian, where (x, t) > 1.