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Manifolds of Critical Points in a Quasilinear Model for Phase Transitions

Citace: [] DRÁBEK, P., MANÁSEVICH, R., TAKÁČ, P. Manifolds of Critical Points in a Quasilinear Model for Phase Transitions. In Nonlinear Elliptic Partial Differential Equations : [Contemporary Mathematics. Vol. 540]. Providence, Rhode Island: American Mathematical Society, 2011. s. 95-134. ISBN: 978-0-8218-4907-1 , ISSN: 0271-4132
Druh: STAŤ VE SBORNÍKU
Jazyk publikace: eng
Anglický název: Manifolds of Critical Points in a Quasilinear Model for Phase Transitions
Rok vydání: 2011
Místo konání: Providence, Rhode Island
Název zdroje: American Mathematical Society
Autoři: Prof. RNDr. Pavel Drábek DrSc. , Prof. Raúl Manásevich PhD. , Prof. Petr Takáč PhD.
Abstrakt CZ: Jsou dokázána tvrzení o exostenci variet kritických bodů funkcionálu energie přiřazeného bistabilní rovnici s pomalou a rychlou difúzí a s nehladkým potenciálem.
Abstrakt EN: We show striking differences in pattern formation produced by the Cahn-Hilliard model with the p-Laplacian and a C1,? potential (0 < ? ? 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.
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