Show simple item record Hieber, Matthias Wood, Ian 2007-11-16T13:38:15Z 2007-11-16T13:38:15Z 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 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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