Communications in Mathematical Physics

, Volume 148, Issue 1, pp 189–208

Global existence and exponential stability of small solutions to nonlinear viscoelasticity

  • S. Kawashima
  • Y. Shibata

DOI: 10.1007/BF02102372

Cite this article as:
Kawashima, S. & Shibata, Y. Commun.Math. Phys. (1992) 148: 189. doi:10.1007/BF02102372


The global existence of smooth solutions to the equations of nonlinear hyperbolic system of 2nd order with third order viscosity is shown for small and smooth initial data in a bounded domain ofn-dimensional Euclidean space with smooth boundary. Dirichlet boundary condition is studied and the asymptotic behaviour of exponential decay type of solutions ast tending to ∞ is described. Time periodic solutions are also studied. As an application of our main theorem, nonlinear viscoelasticity, strongly damped nonlinear wave equation and acoustic wave equation in viscous conducting fluid are treated.

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • S. Kawashima
    • 1
  • Y. Shibata
    • 2
  1. 1.Department of Applied Science, Faculty of Engineering 36Kyushu UniversityFukuokaJapan
  2. 2.Institute of MathematicsUniversity of TsukubaTsukuba-shi, IbarakiJapan