Remarks on blow-up phenomena in p-Laplacian heat equation with inhomogeneous nonlinearity

TL;DR

This paper studies the blow-up behavior of solutions to a p-Laplacian heat equation with inhomogeneous nonlinearity, providing conditions for blow-up and estimates for blow-up time.

Contribution

It offers new blow-up criteria and bounds for the p-Laplacian heat equation with inhomogeneous nonlinearities using differential inequalities.

Findings

Established blow-up conditions based on $\

$ abla$ and initial data.

Derived upper bounds for blow-up time in various cases.

Abstract

We investigate the $p-$Laplace heat equation $u_t-\Delta_p u=\zeta(t)f(u)$ on a bounded smooth domain $\Omega\subset\mathbb{R}^N$. Using differential inequalities arguments, we prove blow-up results under suitable conditions on $\zeta, f$, and the initial data $u_0$. We also give an upper bound for the blow-up time in each case.