Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 40, Issue 9, Pages 1705-1747Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2014.998837
Keywords
Cross diffusion; Duality lemma; Entropy method; Global-in-time existence; Population dynamics; SKT model; Strongly coupled parabolic systems; 35K51; 35K55; 35Q92; 95D25
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Funding
- French ANR blanche project Kibord [ANR-13-BS01-0004]
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This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the cross diffusions is convex, while the other one is concave. The treatment of such cases involves a general study of the structure of Lyapunov functionals for cross diffusion systems, and the introduction of a new scheme of approximation, which provides simplified proofs of existence.
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