On Blow-up of A Reaction Diffusion System Coupled in Both Equations and Boundary Conditions

TL;DR

This paper investigates the blow-up behavior of a reaction diffusion system with coupled equations and boundary conditions, analyzing how reaction and absorption terms influence blow-up properties, including rates and blow-up set characterization.

Contribution

It provides new bounds for blow-up rates and characterizes the blow-up set in coupled reaction diffusion systems under specific assumptions.

Findings

Derived lower and upper bounds for blow-up rates

Identified conditions affecting the blow-up set

Analyzed the influence of reaction and absorption terms

Abstract

We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We derive the lower and upper bound for the blow-up rate, and find the blow-up set under certain assumptions.