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Duality and entropy methods for reversible reaction‐diffusion equations with degenerate diffusion
Author(s) -
Desvillettes L.,
Fellner K.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3407
Subject(s) - degenerate energy levels , mathematics , reaction–diffusion system , duality (order theory) , diffusion , smoothness , entropy (arrow of time) , statistical physics , mathematical analysis , pure mathematics , mathematical physics , thermodynamics , physics , quantum mechanics
A combination of entropy and duality methods has been successfully used in the past to study the existence and smoothness of reaction–diffusion equations arising in reversible chemistry in many situations, but in general under the requirement that the diffusion is non‐degenerate (or at least that all diffusion coefficients are strictly positive a.e.). Here, we wish to describe how these methods also enable to treat reaction–diffusion systems which are strongly degenerate in the sense that one or more of the species do not diffuse at all. Copyright © 2015 JohnWiley & Sons, Ltd.