Global existence for coupled reaction-diffusion equations with a balance law and nonlinearities with non-constant sign

TL;DR

This paper establishes the global existence of solutions for coupled reaction-diffusion equations with a balance law and nonlinearities of variable sign, using Lyapunov techniques to handle unbounded components.

Contribution

It introduces novel Lyapunov-based methods to prove global existence for coupled reaction-diffusion systems with nonlinearities that can change sign.

Findings

Proved global existence under non-constant sign nonlinearities.

Developed Lyapunov techniques for unbounded solution components.

Extended analysis to cases with unbounded solution components.

Abstract

This paper aims to prove the global existence of solutions for coupled reaction diffusion equations with a balance Law and nonlinearities with a non constant sign. The case when one (or both) of the components of the solution is not a priori bounded is treated. Proofs are based on developed Lyapunov techniques.