期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 224, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2022.113092
关键词
Cross diffusion; Size exclusion; Volume filling; Gradient-flow structure; Degenerate nonlinear mobility; Weak-strong stability; Large-data weak solutions; Long-time asymptotics; Relative entropy; Convexity
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. This article aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour, as well as provides a weak-strong stability estimate for a wide range of coefficients.
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour. Second, it provides a weak-strong stability estimate for a wide range of coefficients, which had been missing so far. In order to achieve the results mentioned above, we exploit the formal gradient-flow structure of the model with respect to a logarithmic entropy, which leads to best estimates in the full-interaction case, where all cross-diffusion coefficients are non-zero. Those are crucial to obtain the minimal Sobolev regularity needed for a weak-strong stability result. For meaningful cases when some of the coefficients vanish, we provide a novel existence result based on approximation by the full-interaction case. (c) 2022 Elsevier Ltd. All rights reserved.
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