Semilinear degenerate parabolic systems and distributed capacitance models
type: Item
instance of: scholarly article
title: Semilinear degenerate parabolic systems and distributed capacitance models
zbMATH Open document ID: 0874.35058
author: Brooke L. Hollingsworth
author: Ralph E. Showalter
published in: Discrete and Continuous Dynamical Systems
publication date: 1997-10-22T00:00:00Z
review text: The authors deal with a two-scale microstructure model of current flow in a medium with continuously distributed capacitance. The model is extended to include nonlinearities in the conductance across the interface between the local capacitors and the global conducting medium. The operator, describing the model, has the abstact form of a system of degenerate semilinear parabolic equations. The operator \(A\) that arises from a distributed capacitance model is the subgradient of a convex function, i.e., there exists a convex function \(\phi\) such that \(A= \partial\phi\). Then there exists a convex function \(\Phi\) such that the equation of the model is equivalent to an explicit equation of the standard form \(g \in ({d}/{dt}) w + \partial\Phi (w)\), so this problem is parabolic and has the corresponding regularizing effects on the data. Various limiting cases are identified and the corresponding convergence results are obtained by letting selected parameters tend to infinity.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 35K40
zbMATH DE Number: 1010958
zbMATH Keywords: interface
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: dcds.1995.1.59
OpenAlex ID: W2015537469
DOI: 10.3934/DCDS.1995.1.59
description: scientific article; zbMATH DE number 1010958