ATTRACTORS FOR A CAGINALP MODEL WITH A LOGARITHMIC POTENTIAL AND COUPLED DYNAMIC BOUNDARY CONDITIONS

被引：11
|
作者：
Conti, Monica [1 ]
Gatti, Stefania [2 ]
Miranville, Alain [3 ]
机构：
[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy
[2] Univ Modena & Reggio Emilia, Dipartimento Matemat, I-41125 Modena, Italy
[3] Univ Poitiers, Lab Math & Applicat, SP2MI, CNRS,UMR 7348, F-86962 Futuroscope, France
来源：
ANALYSIS AND APPLICATIONS | 2013年 / 11卷 / 06期
关键词：
Caginalp equations; dynamic boundary conditions; logarithmic potential; global attractor; exponential attractor; CAHN-HILLIARD EQUATION; EXPONENTIAL ATTRACTORS; SINGULAR POTENTIALS; SPINODAL DECOMPOSITION; TIME BEHAVIOR; SYSTEM;
D O I：
10.1142/S0219530513500243
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the longtime behavior of the Caginalp phase-field model with a logarithmic potential and dynamic boundary conditions for both the order parameter and the temperature. Due to the possible lack of distributional solutions, we deal with a suitable definition of solutions based on variational inequalities, for which we prove well-posedness and the existence of global and exponential attractors with finite fractal dimension.
引用
收藏
页数：31
相关论文
共 50 条
  • [31] Kac boundary conditions of the logarithmic minimal models
    Pearce, Paul A.
    Tartaglia, Elena
    Couvreur, Romain
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2015,
  • [32] Logarithmic minimal models with Robin boundary conditions
    Bourgine, Jean-Emile
    Pearce, Paul A.
    Tartaglia, Elena
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2016,
  • [33] ROBUST EXPONENTIAL ATTRACTORS FOR COLEMAN-GURTIN EQUATIONS WITH DYNAMIC BOUNDARY CONDITIONS POSSESSING MEMORY
    Shomberg, Joseph L.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [34] On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
    Colli, Pierluigi
    Gilardi, Gianni
    Sprekels, Juergen
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (02) : 972 - 994
  • [35] Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions
    Chorfi, Salah-Eddine
    El Guermai, Ghita
    Maniar, Lahcen
    Zouhair, Walid
    IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2022, 39 (03) : 861 - 891
  • [36] On the boundary conditions applied to the sea-ice coupled model
    Huang, Rui Xin
    Jin, Xiangze
    JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS, 2007, 112 (C4)
  • [37] On a parabolic-elliptic chemotactic model with coupled boundary conditions
    Delgado, Manuel
    Morales-Rodrigo, Cristian
    Suarez, Antonio
    Ignacio Tello, J.
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) : 3884 - 3902
  • [38] Uniform attractors for the non-autonomous p-Laplacian equations with dynamic flux boundary conditions
    Li, Kun
    You, Bo
    BOUNDARY VALUE PROBLEMS, 2013,
  • [39] Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials (vol 343, pg 557, 2008)
    Cherfils, Laurence
    Gatti, Stefania
    Miranville, Alain
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (02) : 1029 - 1030
  • [40] Pullback exponential attractors for the viscous Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions
    You, Bo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 478 (02) : 321 - 344
12345