Mathematical Results on Existence for Viscoelastodynamic Problems with Unilateral Constraints

Abstract

This paper focuses on a damped wave equation and the evolution of a Kelvin–Voigt viscoelastic material, both problems being subject to unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, both problems possess a weak solution which is obtained as the limit of a sequence of solutions of penalized problems; the functional properties of all the traces are precisely identified through Fourier analysis, and this enables us to infer the existence of a strong solution, i.e., a solution satisfying almost everywhere the unilateral conditions.