Asymptotic stability in nonlinear elastic materials with dissipation

This paper is concerned with the effects of dissipation on classical solutions of the displacement and mixed initial-boundary value problems for a nonlinear elastic material. A proof of the asymptotic stability of the null solution in three dimensions is presented and the necessary assumptions are carefully discussed. The derivation of an analogous result for non-zero equilibrium solutions of the one-dimensional problem completes this work.