Periodic Solutions of a Phase-Field Model with Hysteresis

被引：0
作者：
Chen Bin
Sergey A. Timoshin
机构：
[1] Huaqiao University,Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences
[2] Russian Academy of Sciences,Matrosov Institute for System Dynamics and Control Theory
来源：
Applied Mathematics & Optimization | 2022年 / 85卷
关键词：
Evolution system; Hysteresis; Phase transitions; Periodic solutions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region
引用
收藏
相关论文
共 50 条
  • [11] Phase-field models with hysteresis in one-dimensional thermoviscoplasticity
    Krejcí, P
    Sprekels, J
    Stefanelli, U
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2002, 34 (02) : 409 - 434
  • [12] Global solutions to a degenerate solutal phase-field model for the solidification of a binary alloy
    Scheid, JF
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2004, 5 (01) : 207 - 217
  • [13] Γ-limit of a phase-field model of dislocations
    Garroni, A
    Müller, S
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (06) : 1943 - 1964
  • [14] Hysteresis operators in phase-field models of Penrose-Fife type
    Krejčí P.
    Sprekels J.
    Applications of Mathematics, 1998, 43 (3) : 207 - 222
  • [15] PERIODIC SOLUTIONS OF PARABOLIC PROBLEMS WITH HYSTERESIS ON THE BOUNDARY
    Gurevich, Pavel
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (03) : 1041 - 1083
  • [16] Competition of glass and crystal: Phase-field model
    Vasin, Mikhail
    Ankudinov, Vladimir
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (08) : 6798 - 6809
  • [17] Nonlinear driven response of a phase-field crystal in a periodic pinning potential
    Achim, C. V.
    Ramos, J. A. P.
    Karttunen, M.
    Elder, K. R.
    Granato, E.
    Ala-Nissila, T.
    Ying, S. C.
    PHYSICAL REVIEW E, 2009, 79 (01):
  • [18] On the asymptotic behavior of a phase-field model for elastic phase transitions
    Kalies W.D.
    Journal of Dynamics and Differential Equations, 1997, 9 (2) : 289 - 306
  • [19] Periodic solutions to a heat equation with hysteresis in the source term
    Zheng, Jiashan
    Ke, Yuanyuan
    Wang, Yifu
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 69 (02) : 134 - 143
  • [20] Asymptotic justification of the conserved phase-field model with memory
    Felli, V
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2000, 19 (04): : 953 - 976
12345