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Description
  • Studovaný systém nelineárních parabolických rovnic popisuje proces fázových přechodů jako např. tání-tuhnutí. Rovnice pro fázovou proměnnou je charakterizována singulárním potenciálem, který za vhodných podmínek způsobí, že hodnoty fázové proměnné zůstávají od jistého času stejnoměrně vzdálené od čistých fází. Kombinací této separační vlastnosti a Lojasiewiczovy-Simonovy nerovnosti je dokázáno, že každá hladká omezená trajektorie konverguje ke stacionárnímu řešení a je dán odhad rychlosti této konvergence. (cs)
  • We consider a nonlinear parabolic system which governs the evolution of the (relative) temperature .theta. and of an order parameter .chi.. This system describes phase transition phenomena like, e.g., melting-solidification processes. The equation ruling .chi. is characterized by a singular potential W which forces .chi. to take values in the interval [-1,1]. We provide reasonable conditions on W which ensure that, from a certain time on,.chi. stays uniformly away from the pure phases 1 and -1. Combining this separation property with the Łojasiewicz-Simon inequality, we show that any smooth and bounded trajectory uniformly converges to a stationary state and we give an estimate of the decay rate.
  • We consider a nonlinear parabolic system which governs the evolution of the (relative) temperature .theta. and of an order parameter .chi.. This system describes phase transition phenomena like, e.g., melting-solidification processes. The equation ruling .chi. is characterized by a singular potential W which forces .chi. to take values in the interval [-1,1]. We provide reasonable conditions on W which ensure that, from a certain time on,.chi. stays uniformly away from the pure phases 1 and -1. Combining this separation property with the Łojasiewicz-Simon inequality, we show that any smooth and bounded trajectory uniformly converges to a stationary state and we give an estimate of the decay rate. (en)
Title
  • Long Time Behaviour of Solutions to the Caginalp System with Singular Potential
  • Asymptotické chování řešení Caginalpova systému se singulárním potenciálem (cs)
  • Long Time Behaviour of Solutions to the Caginalp System with Singular Potential (en)
skos:prefLabel
  • Long Time Behaviour of Solutions to the Caginalp System with Singular Potential
  • Asymptotické chování řešení Caginalpova systému se singulárním potenciálem (cs)
  • Long Time Behaviour of Solutions to the Caginalp System with Singular Potential (en)
skos:notation
  • RIV/67985840:_____/06:00044565!RIV07-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 51;72
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(IAA1019302), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 483595
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/06:00044565
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • phase-field models; maximal monotone operators; comparison principle (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [B1DA6B256C23]
http://linked.open...i/riv/nazevZdroje
  • Zeitschrift für Analysis und Ihre Anwendungen
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 25
http://linked.open...iv/tvurceVysledku
  • Petzeltová, Hana
  • Schimperna, G.
  • Grasselli, M.
http://linked.open...n/vavai/riv/zamer
issn
  • 0232-2064
number of pages
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