Blow-up phenomena for a reaction diffusion equation with special diffusion process

TL;DR

This paper investigates the conditions under which solutions to a reaction diffusion equation with special diffusion processes blow up in finite time, providing bounds for the blow-up time using mathematical inequalities and potential well methods.

Contribution

It introduces new analytical techniques to establish blow-up conditions and bounds for a reaction diffusion equation with unique diffusion processes.

Findings

Solutions blow up in finite time under certain initial data conditions.

Derived explicit upper and lower bounds for the blow-up time.

Used Hardy inequality and potential well methods for analysis.

Abstract

This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, by combining Hardy inequality, "moving" potential well methods with some differential inequalities. Moreover, the upper and lower bounds for the blow-up time are also derived when blow-up occurs.