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Evolution equations with dynamic boundary conditions


Hintermann, Thomas (1989). Evolution equations with dynamic boundary conditions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 113(1-2):43-60.

Abstract

SynopsisIn this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems<jats:italic>x</jats:italic>–<jats:italic>Cx</jats:italic>=<jats:italic>f</jats:italic>and<jats:italic>x</jats:italic>(0) =<jats:italic>x</jats:italic><jats:sub>0</jats:sub>. Abstract theoretical results concerning the operators<jats:italic>C</jats:italic>are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.

Abstract

SynopsisIn this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems<jats:italic>x</jats:italic>–<jats:italic>Cx</jats:italic>=<jats:italic>f</jats:italic>and<jats:italic>x</jats:italic>(0) =<jats:italic>x</jats:italic><jats:sub>0</jats:sub>. Abstract theoretical results concerning the operators<jats:italic>C</jats:italic>are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:1 January 1989
Deposited On:18 Oct 2018 08:05
Last Modified:15 Apr 2021 14:50
Publisher:Cambridge University Press
ISSN:0308-2105
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s0308210500023945

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