期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 169, 期 -, 页码 94-117出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2017.12.003
关键词
Cross-diffusion systems; Nonlocal interaction; JKO scheme
资金
- Italian INdAM GNAMPA
- local fund of the University of L'Aquila DP-LAND
- Erasmus Mundus programme MathMods
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform coerciveness assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan-Kinderlehrer-Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure. (C) 2017 Elsevier Ltd. All rights reserved.
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