LONG-TIME BEHAVIOR OF SOLUTIONS TO A CLASS OF FORWARD-BACKWARD PARABOLIC EQUATIONS

被引：14
|
作者：
Smarrazzo, Flavia [1 ]
Tesei, Alberto [1 ]
机构：
[1] Univ Roma La Sapienza, Dept Math G Castelnouvo, I-00185 Rome, Italy
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 03期
关键词：
forward-backward parabolic equations; regularization; Young measures; entropy inequalities; long-time behavior of solutions; steady states; CAHN-HILLIARD EQUATIONS; DIFFUSION EQUATION; HEAT-EQUATION; LIMIT; REGULARIZATION; PARAMETER; EXISTENCE; DIRECTION; MODEL; FLOW;
D O I：
10.1137/090763561
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider weak entropy measure-valued solutions of the Neumann initial-boundary value problem for the equation u(t) = [phi(u)](xx), where phi is nonmonotone. These solutions are obtained from the corresponding problem for the regularized equation u(t) = [phi(u)](xx) vertical bar epsilon u(xxt) (epsilon > 0) by a vanishing viscosity method and satisfy a family of suitable entropy inequalities. Relying on a strong version of these inequalities, we prove exhaustive results concerning the long-time behavior of solutions.
引用
收藏
页码：1046 / 1093
页数：48
相关论文
共 50 条
  • [1] Long-time behaviour of two-phase solutions to a class of forward-backward parabolic equations
    Smarrazzo, Flavia
    INTERFACES AND FREE BOUNDARIES, 2010, 12 (03) : 369 - 408
  • [2] ON A CLASS OF FORWARD-BACKWARD PARABOLIC EQUATIONS: PROPERTIES OF SOLUTIONS
    Bertsch, Michiel
    Smarrazzo, Flavia
    Tesei, Alberto
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (03) : 2037 - 2060
  • [3] On a class of forward-backward parabolic equations: Existence of solutions
    Bertsch, Michiel
    Smarrazzo, Flavia
    Tesei, Alberto
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 177 : 46 - 87
  • [4] Nonuniqueness of solutions for a class of forward-backward parabolic equations
    Bertsch, Michiel
    Smarrazzo, Flavia
    Tesei, Alberto
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 137 : 190 - 212
  • [5] LONG-TIME BEHAVIOR OF SOLUTIONS OF A CLASS OF SEMILINEAR PARABOLIC EQUATIONS
    ROQUEJOFFRE, JM
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 316 (05): : 461 - 464
  • [6] On Lipschitz solutions for some forward-backward parabolic equations
    Kim, Seonghak
    Yan, Baisheng
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (01): : 65 - 100
  • [7] Forward-backward parabolic equations and their time delay approximations
    Horstmann, D
    EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, 2005, : 1089 - 1091
  • [8] LONG-TIME BEHAVIOR FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS
    Li, Hongtao
    Ma, Shan
    Zhong, Chengkui
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (07) : 2873 - 2892
  • [9] Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients
    Chueshov, Igor D.
    Vuillermot, Pierre-A.
    Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 15 (02): : 191 - 232
  • [10] Global existence and long-time behavior of solutions to a class of degenerate parabolic equations
    Anh, Cung The
    Hung, Phan Quoc
    ANNALES POLONICI MATHEMATICI, 2008, 93 (03) : 217 - 230
12345