Homogenization of a one-dimensional diffusion - discrete absorption equation with feedback

The paper is devoted to the diffusion equation with discrete absorption described by a sum of Dirac -functions. Their supports are located at the nodes of some regular grid with the distance between them determined by the integral of solution. This model describes contraction of biological tissue wh...

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Bibliographic Details
Published inApplicable analysis Vol. 95; no. 7; pp. 1507 - 1516
Main Authors Panasenko, Grigory, Volpert, Vitaly
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.07.2016
Taylor & Francis Ltd
Subjects
35B27
Absorption
Analysis of PDEs
Constraining
Consumption
Convergence
Diffusion
Diffusion-discrete absorption equation with feedback
existence of solution
Homogenization
Homogenizing
Mathematical analysis
Mathematical models
Mathematics
35C20
35Q53
existence of solution
homogenization AMS SUBJECT CLASSIFICATIONS 35B27
Diffusion-discrete absorption equation with feedback
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2016.1179288

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Summary:The paper is devoted to the diffusion equation with discrete absorption described by a sum of Dirac -functions. Their supports are located at the nodes of some regular grid with the distance between them determined by the integral of solution. This model describes contraction of biological tissue when cells consume some substance influencing their interaction. In the one-dimensional formulation we prove existence of solutions of the discrete problem and their convergence to the solution of the limiting homogenized problem.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2016.1179288