Parabolic regularization of differential inclusions and the stop operator
type: Item
instance of: scholarly article
title: Parabolic regularization of differential inclusions and the stop operator
zbMATH Open document ID: 1020.35109
DOI: 10.4171/IFB/68
published in: Interfaces and Free Boundaries
publication date: 2003-03-13T00:00:00Z
review text: Parabolic differential inclusion with a set-valued term and a small ``diffusion'' coefficient \(\varepsilon\) at the elliptic operator is considered. The set-valued term is the subdifferential of the indicator function of a convex closed set in a finite-dimensional space. Along with the original inclusion the singular limit inclusion is considered, too. Under used assumptions the existence and the uniqueness of solutions for these inclusions are established. The strong convergence of solutions as \(\varepsilon\to 0\) to the solution of the singular limit inclusion is proved and the connection to elementary hysteresis operators is shown. The approach is based on a suitable penalty approximation. This problem arises for instance in multicomponent phase-field systems.
reviewed by: A. A. Tolstonogov
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35R70
zbMATH DE Number: 1869578
zbMATH Keywords: parabolic differential inclusions
zbMATH Keywords: indicator function
zbMATH Keywords: singular limit
zbMATH Keywords: hysteresis operator
author: Pavel Krejč{í }
author: Jürgen Sprekels
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/68
OpenAlex ID: W2063168735
description: scientific article; zbMATH DE number 1869578