Eigenfunction Expansion Solutions of the Linear Viscoelastic Wave Equation

In this talk we discuss the solution of the elastodynamic

equations in a bounded domain with hereditary-type linear

viscoelastic constitutive relation. Existence, uniqueness, and

regularity of solutions to this problem is demonstrated

for those viscoelastic relaxation tensors satisfying the condition

of being completely monotone. We then consider the non-self-adjoint

and non-linear eigenvalue problem associated with the

frequency-domain form of the elastodynamic equations, and show how

the time-domain solution of the equations can be expressed in

terms of an eigenfunction expansion.