Traveling wave solutions of reaction-diffusion equations with x-dependent combustion type nonlinearities
| dc.contributor.advisor | Schweizer, Ben | |
| dc.contributor.author | Badke, Sven | |
| dc.contributor.referee | Röger, Matthias | |
| dc.date.accepted | 2016-04-27 | |
| dc.date.accessioned | 2016-05-12T12:26:21Z | |
| dc.date.available | 2016-05-12T12:26:21Z | |
| dc.date.issued | 2016-03 | |
| dc.description.abstract | We investigate the existence and uniqueness of traveling wave solutions of the reaction-diffusion equation in periodic heterogeneous media. The reaction-diffusion equation is considered in nondivergence form with no first order term. Our traveling wave problem is considered in similar form in [1] by Xin in the special case that the reaction-term is given by a combustion nonlinearity ƒ = ƒ(u). We prove the existence of traveling wave solutions in case of a class of nonlinearities ƒ = ƒ(x, u), which are a generalization of a combustion nonlinearity. In particular, ƒ is allowed to depend explicitly on x. In case of an additional assumption on ƒ, we also prove a monotonicity result and a uniqueness result. References [1] X. Xin. Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity. Indiana Univ. Math. J., 40(3):985–1008, 1991. | |
| dc.identifier.uri | http://hdl.handle.net/2003/34963 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-17011 | |
| dc.language.iso | en | de |
| dc.subject | Traveling wave | en |
| dc.subject | Reaction-diffusion equation | en |
| dc.subject | Combustion nonlinearity | en |
| dc.subject.ddc | 510 | |
| dc.title | Traveling wave solutions of reaction-diffusion equations with x-dependent combustion type nonlinearities | en |
| dc.type | Text | de |
| dc.type.publicationtype | doctoralThesis | en |
| dcterms.accessRights | open access |