About: Manifolds of Critical Points in a Quasilinear Model for Phase Transitions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We show striking differences in pattern formation produced by the Cahn-Hilliard model with the p-Laplacian and a C1,mý potential (0 { mý ? 1) in place of the regular (linear) Laplace operator and a C2 potential. The corresponding energy functional exhibits multi-dimensional continua (?polyhedra?) of critical points as opposed to the classical case with the Laplace operator. Each of these continua is a finite-dimensional, compact C1,1 manifold with boundary. Some of the critical points are local minimizers of the energy functional in the topology of the Sobolev space W1,p(0, 1), whereas others are only saddle points. The former are interior points of the corresponding continuum (viewed as a compact manifold with boundary), while the latter are boundary points. For the dynamical system generated by the corresponding time-dependent parabolic problem, these facts offer an explanation of the ?slow dynamics? near the continua. We show striking differences in pattern formation produced by the Cahn-Hilliard model with the p-Laplacian and a C1,mý potential (0 { mý ? 1) in place of the regular (linear) Laplace operator and a C2 potential. The corresponding energy functional exhibits multi-dimensional continua (?polyhedra?) of critical points as opposed to the classical case with the Laplace operator. Each of these continua is a finite-dimensional, compact C1,1 manifold with boundary. Some of the critical points are local minimizers of the energy functional in the topology of the Sobolev space W1,p(0, 1), whereas others are only saddle points. The former are interior points of the corresponding continuum (viewed as a compact manifold with boundary), while the latter are boundary points. For the dynamical system generated by the corresponding time-dependent parabolic problem, these facts offer an explanation of the ?slow dynamics? near the continua. (en)
Title	Manifolds of Critical Points in a Quasilinear Model for Phase Transitions Manifolds of Critical Points in a Quasilinear Model for Phase Transitions (en)
skos:prefLabel	Manifolds of Critical Points in a Quasilinear Model for Phase Transitions Manifolds of Critical Points in a Quasilinear Model for Phase Transitions (en)
skos:notation	RIV/49777513:23520/11:43898316!RIV12-MSM-23520___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(MEB100902), Z(MSM4977751301)
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Drábek, Pavel
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	210437
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/11:43898316
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	generalized Cahn-Hilliard and bi-stable equations, p-Laplacian,nonunique continuation for the spatial problem, phase plane analysis, first integral, uniquenessfor the gradient flow, manifolds of critical points. (en)
http://linked.open.../riv/klicoveSlovo	first integral generalized Cahn-Hilliard and bi-stable equations manifolds of critical points. nonunique continuation for the spatial problem phase plane analysis uniquenessfor the gradient flow p-Laplacian
http://linked.open...ontrolniKodProRIV	[605D885AB452]
http://linked.open...v/mistoKonaniAkce	Bruxelles
http://linked.open...i/riv/mistoVydani	Providence, Rhode Island
http://linked.open...i/riv/nazevZdroje	Nonlinear Elliptic Partial Differential Equations : [Contemporary Mathematics. Vol. 540]
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	The Cahn-Hilliard and bi-stable equations in the microscopic theory of phase separation
http://linked.open...UplatneniVysledku	2011
http://linked.open...iv/tvurceVysledku	Drábek, Pavel Manásevich, Raúl Takáč, Petr
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000289967400008
http://linked.open.../riv/zahajeniAkce	2009-09-02 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Spojité a diskrétní matematické struktury a vývoj odpovídajících metod jejich zkoumání
issn	0271-4132
number of pages	40 (xsd:int)
http://purl.org/ne...btex#hasPublisher	American Mathematical Society
https://schema.org/isbn	978-0-8218-4907-1
http://localhost/t...ganizacniJednotka	23520

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