Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (1): 219-236.doi: 10.1016/S0252-9602(12)60014-9

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LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY

Yanni Zeng   

  1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA
  • Received:2011-10-24 Online:2012-01-20 Published:2012-01-20

Abstract:

We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approach-ing to predetermined di?usion waves. Pointwise estimates on the convergence details are obtained.

Key words: hyperbolic systems of balance laws, integro-partial differential equations, viscoelasticity, large time behavior

CLC Number: 

  • 35L65
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