Weak-strong uniqueness for energy-reaction-diffusion systems

TL;DR

This paper proves weak-strong uniqueness and stability for energy-reaction-diffusion systems using a relative entropy method, applicable to thermodynamically consistent models with general reactions.

Contribution

It introduces a novel approach to establish weak-strong uniqueness for a broad class of energy-reaction-diffusion systems based on entropy methods.

Findings

Weak-strong uniqueness holds for dissipative renormalised solutions.

Applicable to models with non-integrable flux and general entropy-dissipating reactions.

Results extend to reaction-cross-diffusion systems.

Abstract

We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. The weak-strong uniqueness principle holds for dissipative renormalised solutions, which in addition to the renormalised formulation obey suitable dissipation inequalities consistent with previous existence results. We treat general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.