Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition

TL;DR

This paper investigates an initial boundary value problem for a semilinear parabolic equation with absorption and a nonlinear nonlocal boundary condition, establishing key theoretical results including comparison principles and conditions for solution uniqueness.

Contribution

It introduces new theoretical results for existence, uniqueness, and nonuniqueness of solutions in semilinear parabolic equations with complex boundary conditions.

Findings

Established comparison principle for the problem

Proved existence of local solutions

Analyzed conditions for uniqueness and nonuniqueness

Abstract

In this paper we consider an initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal Neumann boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of uniqueness and nonuniqueness.