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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
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