Global existence for a strongly coupled reaction diffusion system

TL;DR

This paper proves the global existence and boundedness of solutions for a class of strongly coupled reaction-diffusion systems, extending previous results and verifying them through numerical simulations.

Contribution

It introduces new functional methods to establish global solutions for SKT-type models over a broader parameter range.

Findings

Global existence of solutions for extended parameter ranges

Numerical verification via spectral Galerkin method in 2D

Visualization of system dynamics confirming theoretical results

Abstract

In this work we use functional methods to prove the boundedness and global existence of solutions for a class of strongly coupled parabolic systems. We apply the results to deduce the global existence of solutions for a classic Shigesada-Kawasaki-Teramoto (SKT) type model, for an extended range of the self-diffusion and cross-diffusion coefficients than those available in the current literature. We provide numerical simulations in 2D, via a spectral Galerkin method to verify our global existence results, as well as to visualize the dynamics of the system.