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Evolution equations with dynamic boundary conditions

Published online by Cambridge University Press:  14 November 2011

Thomas Hintermann
Thomas Hintermann
Affiliation:
Mathematisches Institut der Universität Zürich, Rämistrasse 74, CH-8001 Zürich, Switzerland
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Synopsis

In 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 x – Cx = f and x(0) = x0. Abstract theoretical results concerning the operators C 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 1-2 , 1989 , pp. 43 - 60
Copyright
Copyright © Royal Society of Edinburgh 1989

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