# Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems

## TL;DR

This paper establishes the global existence, uniqueness, and exponential stability of solutions for a broad class of nonlinear dissipative systems involving bulk and interface interactions, applicable to complex thermodynamic models.

## Contribution

It introduces a general framework for analyzing nonlinear bulk-interface systems with nonlinear diffusion and coupling, including non-smooth geometries and additional driving mechanisms.

## Key findings

- Proves global well-posedness and stability of solutions.
- Includes nonlinear slow and fast diffusion models.
- Applicable to volume-surface reaction-diffusion systems.

## Abstract

We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface. Additional driving mechanisms can be included and non-smooth geometries and coefficients are admissible, to some extent. An important application are volume-surface reaction-diffusion systems with nonlinear coupled diffusion.