On the Entropic Structure of Reaction-Cross Diffusion Systems
By Laurent Desvillettes, Thomas Lepoutre, Ayman Moussa, Ariane Trescases. 2014
84 citations recorded by the source corpus.
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.
Subfields: Earth-Surface Processes, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/b5411b4d9d512040b6b2258ec5374a4a1431dd5e
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In Earth-Surface Processes
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Citations in the corpus
- The boundedness-by-entropy method for cross-diffusion systems (2015, methodology): “We mention the paper [25] in which the population model with diffusion matrix (12) and functions (14) was investigated and the global existence of weak solutions for general s > 1 was shown.”
- Some variants of the classical Aubin–Lions Lemma (2014, background): “In fact Theorem 1 is already used by the author and some collaborators in the proof of global weak solutions for a reaction/cross-diffusion system, approximated by a similar scheme, see [12] (where Theorem 1 is stated but not proved).”
- Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species (2016, methodology): “This issue can possibly be overcome by employing the scheme proposed in [10] which is specialized to diffusion systems like (5).”