Global existence and exponential stability of small solutions to nonlinear viscoelasticity
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- Kawashima, S. & Shibata, Y. Commun.Math. Phys. (1992) 148: 189. doi:10.1007/BF02102372
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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.