# Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system

## TL;DR

This paper establishes global existence, uniqueness, and regularity for a complex two-species reaction-diffusion system with nonlinear diffusion on volume and surface, utilizing entropic gradient structures to derive bounds.

## Contribution

It introduces a novel approach to prove upper bounds for a reaction-diffusion system with nonlinear bulk and surface diffusion, ensuring well-posedness.

## Key findings

- Proved global existence and uniqueness of solutions.
- Established regularity results for the system.
- Demonstrated the effectiveness of entropic gradient methods.

## Abstract

We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of upper $L^{\infty}$-bounds that exploits the entropic gradient structure of the system.