Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition

TL;DR

This paper investigates the conditions under which solutions to a porous medium equation with absorption and nonlinear nonlocal boundary conditions either exist globally or blow up in finite time.

Contribution

It introduces new results on the existence, comparison principle, and blow-up behavior for this class of porous medium equations with complex boundary conditions.

Findings

Established local existence of solutions.

Proved a comparison principle for solutions.

Demonstrated conditions for global existence and blow-up.

Abstract

In this paper, we consider an initial boundary value problem for the porous medium equation with absorption under a nonlinear nonlocal boundary condition and a nonnegative initial datum. We prove the local existence of solutions, establish a comparison principle, and demonstrate both global existence and blow-up of solutions.