Representation of solutions to wave equations with profile functions
| dc.contributor.author | Lamacz, Agnes | |
| dc.contributor.author | Schweizer, Ben | |
| dc.date.accessioned | 2019-08-05T12:53:43Z | |
| dc.date.available | 2019-08-05T12:53:43Z | |
| dc.date.issued | 2019-05-17 | |
| dc.description.abstract | Solutions 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.identifier.uri | http://hdl.handle.net/2003/38166 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-20145 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Preprint;2019-04 | en |
| dc.subject | large time asymptotics | en |
| dc.subject | wave equation | en |
| dc.subject | effective equation | en |
| dc.subject | dispersion | en |
| dc.subject.ddc | 610 | |
| dc.title | Representation of solutions to wave equations with profile functions | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |