DC FieldValueLanguage
dc.contributor.authorLamacz, Agnes-
dc.contributor.authorSchweizer, Ben-
dc.date.accessioned2019-08-05T12:53:43Z-
dc.date.available2019-08-05T12:53:43Z-
dc.date.issued2019-05-17-
dc.identifier.urihttp://hdl.handle.net/2003/38166-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-20145-
dc.description.abstractSolutions to the wave equation with constant coefficients in $\mathbb{R}^d$ ca be represented explicitly in Fourier space. We investigate a reconstruction formula, which provides an approximation of solutions $u(., t)$ to initial data $u_0(.)$ for large times. The reconstruction consists of three steps: 1) Given $u_0$, initial data for a profile equation are extracted. 2) A profile evolution equation determines the shape of the profile at time $\tau = \varepsilon^2 t$. 3) A shell reconstruction operator transforms the profile to a function on $\mathbb{R}^d$. The sketched construction simplifies the wave equation, since only a one-dimensional problem in an $O(1)$ time span has to be solved. We prove that the construction provides a good approximation to the wave evolution operator for times $t$ of order $\varepsilon^{-2}$.en
dc.language.isoen-
dc.relation.ispartofseriesPreprint;2019-04en
dc.subjectlarge time asymptoticsen
dc.subjectwave equationen
dc.subjecteffective equationen
dc.subjectdispersionen
dc.subject.ddc610-
dc.titleRepresentation of solutions to wave equations with profile functionsen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access-