Weak-strong uniqueness for energy-reaction-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.