Uniqueness of strong solutions and weak–strong stability in a system of cross-diffusion equations

Berendsen J, Burger M, Ehrlacher V, Pietschmann JF (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Evolution Equations Springer Verlag (Germany)

DOI: 10.1007/s00028-019-00534-4

Abstract

Proving the uniqueness of solutions to multi-species cross-diffusion systems is a difficult task in the general case, and there exist very few results in this direction. In this work, we study a particular system with zero-flux boundary conditions for which the existence of a weak solution has been proven in Ehrlacher and Bakhta (ESAIM Math Model Numer Anal, 2017). Under additional assumptions on the value of the cross-diffusion coefficients, we are able to show the existence and uniqueness of non-negative strong solutions. The proof of the existence relies on the use of an appropriate linearized problem and a fixed-point argument. In addition, a weak–strong stability result is obtained for this system in dimension one which also implies uniqueness of weak solutions.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Technische Universität Chemnitz DE Germany (DE) CERMICS – Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique FR France (FR)

How to cite

APA:

Berendsen, J., Burger, M., Ehrlacher, V., & Pietschmann, J.F. (2019). Uniqueness of strong solutions and weak–strong stability in a system of cross-diffusion equations. Journal of Evolution Equations. https://doi.org/10.1007/s00028-019-00534-4

MLA:

Berendsen, Judith, et al. "Uniqueness of strong solutions and weak–strong stability in a system of cross-diffusion equations." Journal of Evolution Equations (2019).

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