WIAS Preprint No. 2808, (2021)

Weak-strong uniqueness for energy-reaction-diffusion systems


  • Hopf, Katharina
    ORCID: 0000-0002-6527-2256

2020 Mathematics Subject Classification

  • 35A02 35K51 35K57 35Q79


  • Energy-reaction-diffusion systems, weak-strong uniqueness, entropy method, convexity method, renormalized solutions, cross diffusion




We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. 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. Weak-strong uniqueness is obtained for 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.

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