New reciprocal and continuous dependence theorems in linear theory of viscoelasticity

Abstract

In this paper we establish new uniqueness and continuous data dependence theorems appropriate to the fundamental dynamic and quasi-static boundary value problems in linear theory of viscoelasticity. On the basis of Lagrange identity and weight function methods, we obtain the results for bounded regions as well as for exterior unbounded regions without definiteness conditions on the initial elasticity and the equilibrium modulus and without recourse to conservation law of energy. Moreover, we use the Lagrange identity to obtain new reciprocal relations for dynamic and quasi-static boundary value problems.