About: A nonlocal phase-field system with inertial term

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study a phase-field system where the energy balance equation has the standard (parabolic) form, while the kinetic equation ruling the evolution of the order parameter X is a nonlocal and nonlinear second-order ODE. The main features of the latter equation are a space convolution term which models long-range interactions of particles and a singular configuration potential that forces X to take values in (-1,1). We first prove the global existence and uniqueness of a regular solution to a suitable initial and boundary value problem associated with the system. Then, we investigate its long time behavior from the point of view of .omega.-limits. In particular, using a nonsmooth version of the Lojasiewicz-Simon inequality, we show that the .omega.-limit of any trajectory contains one and only one stationary solution, provided that the configuration potential in the kinetic equation is convex and analytic. We study a phase-field system where the energy balance equation has the standard (parabolic) form, while the kinetic equation ruling the evolution of the order parameter X is a nonlocal and nonlinear second-order ODE. The main features of the latter equation are a space convolution term which models long-range interactions of particles and a singular configuration potential that forces X to take values in (-1,1). We first prove the global existence and uniqueness of a regular solution to a suitable initial and boundary value problem associated with the system. Then, we investigate its long time behavior from the point of view of .omega.-limits. In particular, using a nonsmooth version of the Lojasiewicz-Simon inequality, we show that the .omega.-limit of any trajectory contains one and only one stationary solution, provided that the configuration potential in the kinetic equation is convex and analytic. (en) Studujeme model fázového pole, kde kinetická rovnice, popisující evoluci fázové proměnné, je nelokální nelineární ODR druhého řádu. Jejím hlavním rysem je prostorová konvulace, která modeluje interakce částic a singulární potenciál, který nutí fázovou proměnnou zůstat v intervalu (-1,1). Je dokázána existence a jednoznačnost řešení počáteční a okrajové úlohy. Dále je dokázáno aplikací nehladké verze Lojasiewiczovy-Simonovy nerovnosti, že omega-limitní množina každé trajektorie je tvořena jediným stacionárním řešením za předpokladu analytičnosti a konvexity nelineárního potenciálu. (cs)
Title	A nonlocal phase-field system with inertial term A nonlocal phase-field system with inertial term (en) Nelokální model fázového pole s inerciálním členem (cs)
skos:prefLabel	A nonlocal phase-field system with inertial term A nonlocal phase-field system with inertial term (en) Nelokální model fázového pole s inerciálním členem (cs)
skos:notation	RIV/67985840:_____/07:00085563!RIV08-AV0-67985840
http://linked.open.../vavai/riv/strany	451;469
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190606), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Petzeltová, Hana
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	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	408034
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/07:00085563
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	nonlocal phase-field system; Lojasiewicz inequality; convergence to equilibria (en)
http://linked.open.../riv/klicoveSlovo	Lojasiewicz inequality convergence to equilibria nonlocal phase-field system
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[2A4C4E25249B]
http://linked.open...i/riv/nazevZdroje	Quarterly of Applied Mathematics
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	Asymptotic analysis of infinite-dimensional dynamical systems
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	65
http://linked.open...iv/tvurceVysledku	Petzeltová, Hana Schimperna, G. Grasselli, M.
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0033-569X
number of pages	19 (xsd:int)
is http://linked.open...avai/riv/vysledek of	A nonlocal phase-field system with inertial term A nonlocal phase-field system with inertial term A nonlocal phase-field system with inertial term

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