Global Existence and Regularity Results for Large Cross Diffusion Models on Planar Domains

TL;DR

This paper proves the global existence of classical solutions for large cross diffusion systems with more than two equations on planar domains, applicable to generalized SKT and food pyramid models with polynomial growth.

Contribution

It establishes the global existence and regularity of solutions for complex cross diffusion systems, extending previous results to models with polynomial growth.

Findings

Proves global existence of solutions for multi-equation cross diffusion systems.

Applicable to generalized SKT and food pyramid models.

Handles polynomial growth in diffusion and reaction terms.

Abstract

The global existence of classical solutions to cross diffusion systems of more than 2 equations given on a planar domain is established. The results can apply to generalized Shigesada-Kawasaki-Teramoto (SKT) and food pyramid models whose diffusion and reaction can have polynomial growth of any order.