Communications in Mathematical Physics

, Volume 148, Issue 1, pp 189-208

First online:

Global existence and exponential stability of small solutions to nonlinear viscoelasticity

  • S. KawashimaAffiliated withDepartment of Applied Science, Faculty of Engineering 36, Kyushu University
  • , Y. ShibataAffiliated withInstitute of Mathematics, University of Tsukuba

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.