Abstract. In this paper we present sufficient conditions for asymptotic stability of a homogeneous equilibrium state of a (nonlinear) elastic body with linear viscosity. The body is subject to external conditions of zero displacements on a part of the boundary, zero surface tractions on the remaining part of the boundary and zero body forces in the interior of the body. The meaning and further qualitative consequence of our conditions are also discussed.
Abstract. In this paper we consider the asymptotic stability of a class of solutions to the mixed initial-boundary value problem in nonlinear thermo-viscoelasticity. The continuum model is a viscoelastic material of rate type with the thermal conduction obeying Fourier's law. The work in this article generalizes in two ways the results obtained by the present authors in a previous paper [1], The results in this present paper are valid for nonisothermal conditions and for a genuinely nonlinear viscous stress.
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