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


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.


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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

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