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| Description
| - We consider the dynamics of the semiflow associated with a class of semilinear parabolic problems on a smooth bounded domain, posed with homogeneous Dirichlet boundary conditions. The distinguishing feature of this class is the indefinite superlinear (but subcritical) growth of the nonlinearity at infinity. We present new a priori bounds for global semiorbits that enable us to give dynamical proofs of known and new existence results for equilibria. In addition, we can prove the existence of connecting orbits in many cases. One advantage of our approach is that the parabolic semiflow is naturally order preserving, in contrast to pseudo-gradient flows considered when using variational methods. Therefore we can obtain much information on nodal properties of equilibria that was not known before.
- We consider the dynamics of the semiflow associated with a class of semilinear parabolic problems on a smooth bounded domain, posed with homogeneous Dirichlet boundary conditions. The distinguishing feature of this class is the indefinite superlinear (but subcritical) growth of the nonlinearity at infinity. We present new a priori bounds for global semiorbits that enable us to give dynamical proofs of known and new existence results for equilibria. In addition, we can prove the existence of connecting orbits in many cases. One advantage of our approach is that the parabolic semiflow is naturally order preserving, in contrast to pseudo-gradient flows considered when using variational methods. Therefore we can obtain much information on nodal properties of equilibria that was not known before. (en)
- Studujeme dynamiku toku asociovaného s třídou semilineárních parabolických problémů na hladké omezené oblasti doplněných homogenní Dirichletovou okrajovou podmínkou. Hlavním znakem studované třídy je indefinitní superlineární (ale podkritický) růst nelinearity v nekonečnu. Ukážeme nové apriorní odhady pro globální semiorbity, které umožňují dokázat některé známé i nové výsledky o existenci ekvilibrií pomocí dynamických metod. V mnoha pripadech navíc ukážeme existenci spojujících orbit. Jedna z výhod našeho přístupu je, že parabolický semitok přirozeně zachovává uspořádání, což kontrastuje s pseudo gradientním tokem, který se používá ve variačních metodách. To umožňuje získat mnoho nových vlastnotí ekvilibrií. (cs)
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| Title
| - A priori bounds, nodal equilibria and connecting orbits in indefinite superlinear parabolic problems
- Apriorní odhady, nodální ekvilibria a spojující orbity pro indefinitní superlineární parabolické problémy (cs)
- A priori bounds, nodal equilibria and connecting orbits in indefinite superlinear parabolic problems (en)
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| skos:prefLabel
| - A priori bounds, nodal equilibria and connecting orbits in indefinite superlinear parabolic problems
- Apriorní odhady, nodální ekvilibria a spojující orbity pro indefinitní superlineární parabolické problémy (cs)
- A priori bounds, nodal equilibria and connecting orbits in indefinite superlinear parabolic problems (en)
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| skos:notation
| - RIV/00216208:11320/08:00100837!RIV09-GA0-11320___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/08:00100837
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - priori; bounds; nodal; equilibria; connecting; orbits; indefinite; superlinear; parabolic; problems (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Transactions of the American Mathematical Society
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Kaplický, Petr
- Ackermann, Nils
- Bartsch, Thomas
- Quittner, Pavol
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| http://linked.open...ain/vavai/riv/wos
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| issn
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| number of pages
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| http://localhost/t...ganizacniJednotka
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