Global Existence of solutions for systems of coupled reaction diffusion equations with nonlinearities of unlimited growth

TL;DR

This paper proves the global existence and boundedness of solutions for 2x2 reaction-diffusion systems with unbounded nonlinearities, applicable to physical-chemistry models, using a novel Lyapunov functional approach.

Contribution

It introduces a new method to establish global solutions for reaction-diffusion systems with unlimited growth nonlinearities without restrictions on diffusion or initial data.

Findings

Solutions are globally existent and uniformly bounded.

Results apply to systems with nonlinearities of unlimited growth.

No restrictions on diffusion terms or initial data.

Abstract

In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions on diffusion terms neither on the initial data. Such systems possess many applications in physical-chemistry. Our technique of proof relies on a judiciously rectified Lyapunov functional used previously by the author in several papers