Local solutions to quasilinear parabolic equations without growth restrictions
type: Item
instance of: scholarly article
title: Local solutions to quasilinear parabolic equations without growth restrictions
zbMATH Open document ID: 0851.35051
DOI: 10.4171/ZAA/706
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-06-13T00:00:00Z
review text: Summary: The paper deals with quasilinear parabolic boundary value problems where the nonlinear coefficients and right-hand side are defined with respect to the unknown function \(u= u(x, t)\) only in a neighbourhood of the initial function. The quasilinear parabolic problem is approximated by linear elliptic problems by means of semidiscretization in time. It is proved that the approximations converge uniformly although the data are not continuous functions, and the limit turns out to be the weak solution of the parabolic problem for sufficiently small time \(t\). The crucial points of the paper are \(L_\infty\)-estimates to ensure that the approximations belong to the domain of nonlinearities and uniform estimates of the discrete time derivatives in a Lebesgue space in order to obtain uniform convergence.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 889003
zbMATH Keywords: nonlinear Gronwall lemma
zbMATH Keywords: local solutions
zbMATH Keywords: quasilinear parabolic boundary value problems
zbMATH Keywords: semidiscretization in time
zbMATH Keywords: \(L_ \infty\)-estimates
author: V. Pluschke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 889003