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| Description
| - We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term .CHI.tt, .CHI. being the order parameter, which is linearly coupled with an evolution equation for the (relative) temperature. The latter can be of hyperbolic type if the Cattaneo-Maxwell heat conduction law is assumed. The state variables and the chemical potential are subject to the homogeneous Neumann boundary conditions. We first provide conditions which ensure the well-posedness of the initial and boundary value problem. Then, we prove that the corresponding dynamical system is dissipative and possesses a global attractor. Moreover, assuming that the nonlinear potential is real analytic, we establish that each trajectory converges to a single steady state by using a suitable version of the Łojasiewicz-Simon inequality.
- We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term .CHI.tt, .CHI. being the order parameter, which is linearly coupled with an evolution equation for the (relative) temperature. The latter can be of hyperbolic type if the Cattaneo-Maxwell heat conduction law is assumed. The state variables and the chemical potential are subject to the homogeneous Neumann boundary conditions. We first provide conditions which ensure the well-posedness of the initial and boundary value problem. Then, we prove that the corresponding dynamical system is dissipative and possesses a global attractor. Moreover, assuming that the nonlinear potential is real analytic, we establish that each trajectory converges to a single steady state by using a suitable version of the Łojasiewicz-Simon inequality. (en)
- Studujeme model popisující rychlé fázové separace ve třírozměrné omezené oblasti. Tento model sestává z viskozní Cahn-Hilliardovy rovnice pro fázovou proměnnou nelineárně spojenou s rovnicí pro teplotu, která může být hyperbolického typu, když je uvažován Cattaneo-Maxwellův konstituční zákon. Jsou nalezeny podmínky pro korektně definovanou počáteční úlohu. Dále je dokázáno, že odpovídající dynamický systém je disipativní a existuje globální atraktor. Za předpokladu analytičnosti nelineárního potenciálu je dokázána konvergence každého řešení k jedinému stacionárnímu stavu a odhadnuta rychlost této konvergence. (cs)
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| Title
| - Asymptotic behavior of a nonisothermal viscous Cahn-Hillard equation with inertial term
- Asymptotické chování řešení neizotermální viskozní Cahnovy-Hilliardovy rovnice s inerciálním členem (cs)
- Asymptotic behavior of a nonisothermal viscous Cahn-Hillard equation with inertial term (en)
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| skos:prefLabel
| - Asymptotic behavior of a nonisothermal viscous Cahn-Hillard equation with inertial term
- Asymptotické chování řešení neizotermální viskozní Cahnovy-Hilliardovy rovnice s inerciálním členem (cs)
- Asymptotic behavior of a nonisothermal viscous Cahn-Hillard equation with inertial term (en)
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| skos:notation
| - RIV/67985840:_____/07:00085082!RIV08-AV0-67985840
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(IAA100190606), Z(AV0Z10190503)
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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/67985840:_____/07:00085082
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - fast phase separation; convergence to equilibria; Łojasiewicz inequality (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
| - Journal of Differential Equations
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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
| - Petzeltová, Hana
- Schimperna, G.
- Grasselli, M.
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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| is http://linked.open...avai/riv/vysledek
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