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dc.contributor.authorTrofimchuk, Elena
dc.contributor.authorTkachenko, Victor
dc.contributor.authorTrofimchuk, Sergei I.
dc.date.accessioned2007-03-20T12:00:08Z
dc.date.accessioned2016-10-05T14:14:22Z
dc.date.available2007-03-20T12:00:08Z
dc.date.available2016-10-05T14:14:22Z
dc.date.issued2007-03-28
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1207
dc.descriptionResearch in Pairs 2007en_US
dc.description.abstractWe study positive bounded wave solutions $u(t, x) = \phi(\nu \cdot x+ct)$, $\phi(-\infty)=0$, of equation $u_t(t, x)=\delta u(t,x)−u(t,x) +g(u(t−h,x))$, $x \in \mathbb{R}^m$(*). It is supposed that Eq. (∗) has exactly two non-negative equilibria: $u_1 \equiv 0$ and $u_2 \equiv \kappa>9$. The birth function $g \in C(\mathbb{R}_+, \mathbb{R}_+)$ satisfies a few mild conditions: it is unimodal and differentiable at $0,\kappa$. Some results also require the positive feedback of $g:[g(\text{max} g),\text{max} g] \to \mathbb{R}_+$ with respect to $\kappa$. If additionally $\phi(+\infty) =\kappa$, the above wave solution $u(t,x)$ is called a travelling front. We prove that every wave $\phi(\nu \cdot x+ct)$ is eventually monotone or slowly oscillating about $\kappa$. Furthermore, we indicate $c^∗ \in \mathbb{R}_+ \cup {+\infty}$ such that (∗) does not have any travelling front (neither monotone nor non-monotone) propagating at velocity $c > c^∗$. Our results are based on a detailed geometric description of the wave profile $\phi$. In particular, the monotonicity of its leading edge is established. We also discuss the uniqueness problem indicating a subclass $\mathcal{G}$ of ’asymmetric’ tent maps such that given $g \in \mathcal{G}$, there exists exactly one travelling front for each fixed admissible speed.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2007,12
dc.titleSlowly oscillating wave solutions of a single species reaction-diffusion equation with delayen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2007-12
local.scientificprogramResearch in Pairs 2007
local.series.idOWP-2007-12
local.subject.msc34
local.subject.msc35
local.subject.msc92
dc.identifier.urnurn:nbn:de:101:1-20080627180
dc.identifier.ppn1646163427


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