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Entropy functionals for finding requirements in hierarchical reaction‐diffusion models for inflammations
Author(s) -
Reisch Cordula,
Langemann Dirk
Publication year - 2020
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.6682
Subject(s) - reaction–diffusion system , mathematics , uniqueness , entropy (arrow of time) , pure mathematics , mathematical analysis , thermodynamics , physics
Based on an established model for liver infections, we open the discussion on the used reaction terms in the reaction‐diffusion system. The mechanisms behind the chronification of liver infections are widely unknown, therefore we discuss a variety of reaction functions. By using theorems about existence, uniqueness, and nonnegativity, we identify properties of reaction functions which are indispensable to modelling liver infections. We introduce an entropy functional for reaction‐diffusion models of this type, which allows predictions of the longtime behavior of the solutions. As a result, we find more conditions on the reaction functions to derive a model covering different inflammation courses. Finally, we discuss the models in the frame of a hierarchical model family.