Global smooth solutions for triangular reaction-cross diffusion systems

For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This class of systems arises in Population dynamics, and extends...

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Bibliographic Details
Published in:Bulletin des sciences mathématiques 2023-12, Vol.189, p.103342, Article 103342
Main Authors: Guerand, Jessica, Menegaki, Angeliki, Trescases, Ariane
Format: Article
Language:English
Subjects:
Analysis of PDEs
Cross-diffusion system
De-Giorgi method
Global existence
Global parabolic regularity
Mathematics
SKT system
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Summary:For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This class of systems arises in Population dynamics, and extends the triangular Shigesada-Kawasaki-Teramoto system when general power-laws growth are considered in the reaction and diffusion rates.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2023.103342