• Previous Article
    Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems
  • DCDS-B Home
  • This Issue
  • Next Article
    Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (II) Convergence
June  2007, 7(4): 825-837. doi: 10.3934/dcdsb.2007.7.825

Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness

1. 

Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada

2. 

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

3. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539-2999, United States

Received  June 2006 Revised  January 2007 Published  March 2007

This paper focuses on the phase transitions of a 2$\times$2 system of mixed type for viscosity-capillarity with periodic initial-boundary condition in a viscoelastic material. By the Liapunov functional method, we prove the existence, uniqueness, regularity and uniform boundedness of the solution. The results are correct even for large initial data.
Citation: Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 825-837. doi: 10.3934/dcdsb.2007.7.825
[1]

Ming Mei, Yau Shu Wong, Liping Liu. Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (II) Convergence. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 839-857. doi: 10.3934/dcdsb.2007.7.839

[2]

Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 917-923. doi: 10.3934/dcdss.2014.7.917

[3]

Peng Jiang. Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3015-3037. doi: 10.3934/dcds.2015.35.3015

[4]

Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 59-78. doi: 10.3934/dcds.2005.12.59

[5]

Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initial-boundary value problem. Conference Publications, 2007, 2007 (Special) : 212-220. doi: 10.3934/proc.2007.2007.212

[6]

Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917

[7]

Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381

[8]

Martn P. Árciga Alejandre, Elena I. Kaikina. Mixed initial-boundary value problem for Ott-Sudan-Ostrovskiy equation. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 381-409. doi: 10.3934/dcds.2012.32.381

[9]

Michal Beneš. Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains. Conference Publications, 2011, 2011 (Special) : 135-144. doi: 10.3934/proc.2011.2011.135

[10]

Haifeng Hu, Kaijun Zhang. Analysis on the initial-boundary value problem of a full bipolar hydrodynamic model for semiconductors. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1601-1626. doi: 10.3934/dcdsb.2014.19.1601

[11]

Türker Özsarı, Nermin Yolcu. The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3285-3316. doi: 10.3934/cpaa.2019148

[12]

Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure & Applied Analysis, 2004, 3 (2) : 319-328. doi: 10.3934/cpaa.2004.3.319

[13]

Linglong Du, Caixuan Ren. Pointwise wave behavior of the initial-boundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3265-3280. doi: 10.3934/dcdsb.2018319

[14]

Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks & Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011

[15]

John R. Graef, Lingju Kong, Min Wang. Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Conference Publications, 2013, 2013 (special) : 291-299. doi: 10.3934/proc.2013.2013.291

[16]

Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 431-444. doi: 10.3934/dcds.1998.4.431

[17]

V. A. Dougalis, D. E. Mitsotakis, J.-C. Saut. On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1191-1204. doi: 10.3934/dcds.2009.23.1191

[18]

Shou-Fu Tian. Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval. Communications on Pure & Applied Analysis, 2018, 17 (3) : 923-957. doi: 10.3934/cpaa.2018046

[19]

Runzhang Xu, Mingyou Zhang, Shaohua Chen, Yanbing Yang, Jihong Shen. The initial-boundary value problems for a class of sixth order nonlinear wave equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5631-5649. doi: 10.3934/dcds.2017244

[20]

Mauro Garavello. Boundary value problem for a phase transition model. Networks & Heterogeneous Media, 2016, 11 (1) : 89-105. doi: 10.3934/nhm.2016.11.89

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]