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

TL;DR

This paper investigates the conditions under which solutions to a nonlinear nonlocal parabolic equation with absorption either exist globally or blow up, considering nonlocal boundary conditions and initial data.

Contribution

It establishes comparison principles, and proves both global existence and blow-up results for solutions of the nonlinear nonlocal parabolic problem.

Findings

Comparison principle established

Conditions for global existence proved

Blow-up of solutions demonstrated

Abstract

In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove comparison principle, global existence and blow-up of solutions.