On the Caginalp system with dynamic boundary conditions and singular potentials

Laurence Cherfils; Alain Miranville

Applications of Mathematics (2009)

  • Volume: 54, Issue: 2, page 89-115
  • ISSN: 0862-7940

Abstract

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This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in H 2 , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in order to prove the convergence of solutions to steady states.

How to cite

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Cherfils, Laurence, and Miranville, Alain. "On the Caginalp system with dynamic boundary conditions and singular potentials." Applications of Mathematics 54.2 (2009): 89-115. <http://eudml.org/doc/37811>.

@article{Cherfils2009,
abstract = {This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in $H^2$, the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in order to prove the convergence of solutions to steady states.},
author = {Cherfils, Laurence, Miranville, Alain},
journal = {Applications of Mathematics},
keywords = {Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Łojasiewicz-Simon inequality; convergence to a steady state; Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor},
language = {eng},
number = {2},
pages = {89-115},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Caginalp system with dynamic boundary conditions and singular potentials},
url = {http://eudml.org/doc/37811},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Cherfils, Laurence
AU - Miranville, Alain
TI - On the Caginalp system with dynamic boundary conditions and singular potentials
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 89
EP - 115
AB - This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in $H^2$, the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in order to prove the convergence of solutions to steady states.
LA - eng
KW - Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Łojasiewicz-Simon inequality; convergence to a steady state; Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor
UR - http://eudml.org/doc/37811
ER -

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