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arXiv · 1812.10711

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

Judith Berendsen·Martin Burger·Virginie Ehrlacher·Jan-Frederik Pietschmann
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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 [Ehrlacher2017]. Under additional assumptions on the value of the cross-diffusion coefficients, we are able to show the existence and uniqueness of strong solutions. The proof relies on the use of an appropriate approximation and a fixed-point argument. In addition, a weak-strong stability result is obtained for this system in dimension one.

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Judith Berendsen, Martin Burger, Virginie Ehrlacher, Jan-Frederik Pietschmann. 2018-12-27. Strong solutions and weak-strong stability in a system of cross-diffusion equations. https://arxiv.org/abs/1812.10711

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