数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (1): 219-236.doi: 10.1016/S0252-9602(12)60014-9

• 论文 • 上一篇    下一篇

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
  • 收稿日期:2011-10-24 出版日期:2012-01-20 发布日期:2012-01-20

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

摘要:

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.

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

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

中图分类号: 

  • 35L65