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.issn 1424-3202
dc.identifier.other PURE: 72881
dc.identifier.other PURE UUID: b1feb5d8-544f-4887-ada6-01bb1398ee05
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.rights en
dc.title Asymptotics of Perturbations to the Wave Equation en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.contributor.institution Department of Physics en
dc.contributor.institution Mathematics and Physics en
dc.description.status Peer reviewed en

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