Global existence and blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition

TL;DR

This paper investigates conditions under which solutions to a semilinear heat equation with nonlinear nonlocal boundary conditions exist globally or blow up in finite time, providing new criteria for these behaviors.

Contribution

It introduces new criteria for global existence and blow-up of solutions in semilinear heat equations with nonlinear nonlocal boundary conditions.

Findings

Established conditions for global existence of solutions.

Derived criteria for finite-time blow-up.

Analyzed the influence of initial data on solution behavior.

Abstract

In this paper we consider a semilinear parabolic equation with nonlinear and nonlocal boundary condition and nonnegative initial datum. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given.