# Asymptotics of Perturbations to the Wave Equation

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 dc.contributor.author Hieber, Matthias dc.contributor.author Wood, Ian dc.date.accessioned 2007-11-16T13:38:15Z dc.date.available 2007-11-16T13:38:15Z dc.date.issued 2003 dc.identifier.citation Hieber , M & Wood , I 2003 , ' Asymptotics of Perturbations to the Wave Equation ' Journal of Evolution Equations , pp. 243-252 . en dc.identifier.other PURE: 72881 dc.identifier.other dspace: 2160/360 dc.identifier.uri http://hdl.handle.net/2160/360 dc.identifier.uri http://www.routledge.com/ en dc.description M. Hieber, I. Wood: Asymptotics of perturbations to the wave equation. In: Evolution Equations, Lecture Notes in Pure and Appl. Math., 234, Marcel Dekker, (2003), 243-252. en dc.description.abstract The starting point for this article is a well-known example by M.~Renardy showing the failure of the equality $\omega(T)=s(A)$ for a first order perturbation to the wave equation, where $\omega(T)$ denotes the growth bound of the semigroup $T$ generated by $A$ and $s(A)$ is the spectral bound of $A$. In this article we give conditions on first order perturbations to the wave equation guaranteeing the equality. More specifically, we show that for a class of self-adjoint perturbations the equality of bounds which exists for the wave equation is preserved. Making use of the theory of cosine functions, we are able to extend Renardy's construction of a counterexample to higher order equations. en dc.format.extent 10 en dc.language.iso eng dc.relation.ispartof Journal of Evolution Equations en dc.title Asymptotics of Perturbations to the Wave Equation en dc.type Text en dc.type.publicationtype Article (Journal) en dc.contributor.institution Institute of Mathematics & Physics (ADT) en dc.contributor.institution Mathematics and Physics en dc.description.status Peer reviewed en
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