WAVE PROPAGATION, UNIQUENESS AND SINGULARITIES AT INFINITY FOR AN UNBOUNDED LINEARLY VISCOELASTIC MATERIAL

Abstract

Following a method used in two earlier papers,2,3 a general domain of dependence in equality is proved for inhomogeneous and anisotropic linearly viscoelastic solids, which furnishes the explicit link between the maximum propagation speed of disturbances in the body and the behavior at infinity of the acoustic tensor and the memory functions of the material, and allows to prove a global uniqueness theorem for the mixed problem of viscoelasticity in an unbounded reference configuration Ω. The method of proof applies regardless of whether the memory functions are assumed or not: moreover, no boundedness assumption is made on the material data.