Blow up of solutions for pseudo-parabolic equation with singular potential and variable exponents

TL;DR

This paper investigates the finite time blow-up behavior of solutions to a pseudo-parabolic equation with singular potential and variable exponents, providing bounds on the blow-up time.

Contribution

It introduces analysis of blow-up phenomena for a pseudo-parabolic equation with spatially and temporally variable exponents and singular potentials, which is a novel extension.

Findings

Solutions blow up in finite time under certain conditions.

Upper and lower bounds for blow-up time are established.

The influence of variable exponents on blow-up behavior is characterized.

Abstract

We consider the initial boundary value problem of a pseudo-parabolic equation with singular potential and the exponent $p(x,t)$ depending on both spatial and temporal variables. We prove the finite time blow up and estimate the upper and lower bounds of the blow up time.