Acta mathematica scientia,Series B

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EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION

 RUAN Li-Zhi, SHU Chang-Jiang   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    The research was supported by the Natural Science
    Foundation of China(10171037) and the National Key Program for Basic Research of China(2002CCA03700)
    respectively. The first author was supported by south central university for Nationalities Nature Science Foun-
    dation of China(YZQ03003).

Abstract:

This paper is concerned with the initial boundary value problem for a vis-
coelastic model with relaxation. Under the only assumption that the C0-norm of the
initial data is small, without smallness hypothesis for the C1-norm, the existence of the
global smooth solution to the corresponding initial boundary value problem is proved.
The analysis is based on some a priori estimates obtained by the “maximum principle” of
first-order quasilinear hyperbolic system.

Key words: Viscoelastic model, relaxation;a priori estimates;maximum principle

CLC Number: 

  • 35L50
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