About: An invariant set generated by the domain topology for parabolic semiflows with small diffusion

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Uvažujeme singulárně perturbovaný semilineární parabolický problém u_t-d^2\Delta u+u=f(u) s homogenní Neumannovou okrajovou podmínkou na oblasti \Omega\subseteq{\mathbb{R}}^N s hladkou hranicí. Funkce f je superlineární v 0 a v nekonečnu a má podkritický růst. Pro malé d>0 konstuujeme kompatní, souvislou, invariantní množinu X_d v hranici oblasti přitažlivosti asymptoticky stabilního ekvilibria 0. Hlavní vlastností X_d je, že se skládá z neporovnatelných pozitivních funkcí a jeho topologie je alespoň tak bohatá jako topologie hranice \Omega. Pokud je počet ekvilibrií v X_d konečný, existují spojující orbity v X_d, které nejsou důsledkem známého Matanova výsledku. (cs) We consider the singularly perturbed semilinear parabolic problem u_t-d^2\Delta u+u=f(u) with homogeneous Neumann boundary conditions on a smoothly bounded domain \Omega\subseteq{\mathbb{R}}^N. Here f is superlinear at 0, and infinity and has subcritical growth. For small d>0 we construct a compact connected invariant set X_d in the boundary of the domain of attraction of the asymptotically stable equilibrium $0$. The main features of $X_d$ are that it consists of positive functions that are pairwise non-comparable, and its topology is at least as rich as the topology of $\partial\Omega$ in a certain sense. If the number of equilibria in $X_d$ is finite, then this implies the existence of connecting orbits within $X_d$ that are not a consequence of a well known result by Matano. We consider the singularly perturbed semilinear parabolic problem u_t-d^2\Delta u+u=f(u) with homogeneous Neumann boundary conditions on a smoothly bounded domain \Omega\subseteq{\mathbb{R}}^N. Here f is superlinear at 0, and infinity and has subcritical growth. For small d>0 we construct a compact connected invariant set X_d in the boundary of the domain of attraction of the asymptotically stable equilibrium $0$. The main features of $X_d$ are that it consists of positive functions that are pairwise non-comparable, and its topology is at least as rich as the topology of $\partial\Omega$ in a certain sense. If the number of equilibria in $X_d$ is finite, then this implies the existence of connecting orbits within $X_d$ that are not a consequence of a well known result by Matano. (en)
Title	An invariant set generated by the domain topology for parabolic semiflows with small diffusion Invariantní množina generovaná topologií oblasti pro parabolické polotoky s malou difuzí (cs) An invariant set generated by the domain topology for parabolic semiflows with small diffusion (en)
skos:prefLabel	An invariant set generated by the domain topology for parabolic semiflows with small diffusion Invariantní množina generovaná topologií oblasti pro parabolické polotoky s malou difuzí (cs) An invariant set generated by the domain topology for parabolic semiflows with small diffusion (en)
skos:notation	RIV/00216208:11320/07:00005033!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany	613;628
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/06/0352), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Kaplický, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	409349
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/07:00005033
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	invariant; generated; domain; topology; parabolic; semiflows; small; diffusion (en)
http://linked.open.../riv/klicoveSlovo	domain diffusion invariant small parabolic topology generated semiflows
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[EC2EDE4A3E99]
http://linked.open...i/riv/nazevZdroje	Discrete and Continuous Dynamical Systems
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Incompressible fluids with complex rheology: mathematical analysis, computational simulations and optimization of their flows
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	18
http://linked.open...iv/tvurceVysledku	Kaplický, Petr
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	1078-0947
number of pages	16 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

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