A Lower Bound for the Norm of the Solution of a Nonlinear Volterra Equation in One-Dimensional Viscoelasticity

摘要

It is shown that the lower bound for the norm of sufficiently smooth solutions of initial history value problems associated with the nonlinear, one-dimenstional model of viscoelastic response must grow quadratically in time on any interval where the norm of U is bounded from above. No sign definiteness restrictions are imposed on the derivatives on this model of nonlinear viscoelastic response.