Renormalised solutions to reaction-diffusion systems with interface conditions: Global existence and weak-strong uniqueness
Authors
- Hopf, Katharina
ORCID: 0000-0002-6527-2256 - Tang, Bao Quoc
2020 Mathematics Subject Classification
- 35K51 35K57
Keywords
- Dissipative bulk-interface reaction-diffusion systems, renormalised solutions, relative entropy method, reflection technique, generalised gradient structure
DOI
Abstract
We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to systems coupled by nonlinear interface conditions. For this notion of solution, we establish global existence as well as a weak-strong stability estimate. Our framework allows to handle entropy-dissipating interfacial transmission rates without growth restrictions, including power-law nonlinearities as arising in the thermodynamic modelling of dissipative bulk-interface systems via generalised gradient structures. Our analysis relies on suitable extensions of the species' densities across the interface as well as on a non-local truncated variant of the relative entropy.
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