# American Institute of Mathematical Sciences

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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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