Uniqueness of initial-boundary value problems in nonlocal elasticity

Abstract In this study we have dealt with the uniqueness of the solutions of a class of initial-boundary value problems in linear, isotropic, homogeneous, nonlocal elasticity. The proof of uniqueness is based on the positive definiteness of total strain energy. After giving the sufficient conditions under which total strain energy is positive definite, it has been shown that the solutions of the initial-boundary value problems which are considered in this study are unique. Existence of the solutions of these problems is an a priori assumption.