Regularity and uniqueness in quasilinear parabolic systems.
type: Item
instance of: scholarly article
title: Regularity and uniqueness in quasilinear parabolic systems.
zbMATH Open document ID: 1240.35234
author: Lucia Panizzi
author: Pavel Krejč{í }
published in: Applications of Mathematics
publication date: 2011-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/116544
full work available at URL: http://hdl.handle.net/10338.dmlcz/141598
review text: Inspired by a problem in steel metallurgy, the authors prove the existence, regularity, uniqueness and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma. According to my opinion this is a very nice paper which addresses real world applications and uses modern mathematical methods at the same time.
reviewed by: Pavel Drábek
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 5963755
zbMATH Keywords: parabolic system
zbMATH Keywords: regularity
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
OpenAlex ID: W2018938718
cites work: EXISTENCE, UNIQUENESS AND APPROXIMATION OF A DOUBLY-DEGENERATE NONLINEAR PARABOLIC SYSTEM MODELLING BACTERIAL EVOLUTION
cites work: A MATHEMATICAL MODEL FOR CASE HARDENING OF STEEL
cites work: Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces
cites work: Q4354424
cites work: A NONLINEAR PARABOLIC SYSTEM ARISING IN THERMOMECHANICS AND IN THERMOMAGNETISM
cites work: Classical solvability of the coupled system modelling a heat-convergent Poiseuille-type flow
DOI: 10.1007/S10492-011-0020-5
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description: scientific article; zbMATH DE number 5963755