Blow-up phenomena for a reaction-diffusion equation with a singular coefficient

reaction-diffusion equation with a singular coefficient

Résumé

In this paper, we investigate a reaction-diffusion equation with a singular coefficient that is relevant to various physical models and includes an initial boundary value problem. We investigate the scenarios of sub-critical, critical, and supercritical initial energy levels.

We provide estimates for both the lower and upper bounds of the blow-up time and establish a blow-up result for cases with sub-critical initial energy. Additionally, we examine finite-time blow-up, show global existence, illustrate asymptotic behavior, and present a lower bound for blow-up time in the context of critical initial energy. Finally, we estimate the lower and upper bounds of blow-up time and illustrate the existence of finite-time blow-up for supercritical initial energy. Our research builds upon and extends previous studies in this field.