Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems

Philippe Laurençot and Bogdan-Vasile Matioc

Address:
Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS F–31062 Toulouse Cedex 9, France
Fakultät für Mathematik, Universität Regensburg D–93040 Regensburg, Deutschland

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Abstract: Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.

AMSclassification: primary 35A02; secondary 35K51, 35K65, 35Q35.

Keywords: cross diffusion, weak-strong uniqueness, relative entropy.

DOI: 10.5817/AM2023-2-201