Quasilinear parabolic systems under nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Quasilinear parabolic systems under nonlinear boundary conditions
zbMATH Open document ID: 0596.35061
DOI: 10.1007/BF00251255
author: Herbert Amann
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The author proves existence and regularity results for abstract quasilinear parabolic systems of the form \[ (*)\quad \partial u/\partial t+A(t,u)u=f(t,u),\quad B(t,u)u=g(t,u),\quad u(s)=u_ 0\quad for\quad s<t\leq T. \] An important example for which his results are applicable is the case of elliptic operators \[ A(t,u)u:=-D_ j(a_{jk}(\cdot,t,u)D_ ku)+a_ j(\cdot,t,u)D_ ju. \] A great variety of problems in applications lead to a system of the form (*). The wide range of applications of the author's results emphasize the importance of this paper.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35R15
zbMATH DE Number: 3960083
zbMATH Keywords: quasilinear evolution equations
zbMATH Keywords: existence
zbMATH Keywords: regularity
zbMATH Keywords: abstract quasilinear parabolic systems
reviewed by: Robert L. Taylor
MaRDI profile type: Publication
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
cites work: Dual semigroups and second order linear elliptic boundary value problems
cites work: Q3027518
cites work: Global existence for semilinear parabolic systems.
cites work: Quasilinear Evolution Equations and Parabolic Systems
cites work: On abstract parabolic fundamental solutions
cites work: Q4597625
cites work: An optimal regularity result for a class of quasilinear parabolic systems
cites work: On the partial regularity of weak solutions on nonlinear parabolic systems
cites work: Remarks on pseudo-resolvents and infinitesimal generators of semi-groups
cites work: Q3291810
cites work: Fractional powers of operators
cites work: Q5628582
cites work: Norms and Domains of the Complex Powers A B z
cites work: Q3692155
cites work: Q3689568
cites work: Q3207428
cites work: Q4169289
cites work: On the abstract linear evolution equations in Banach spaces
cites work: On the abstract evolution equation of parabolic type
cites work: Analyticity of solutions of quasilinear evolution equations
cites work: Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces
description: scientific article; zbMATH DE number 3960083