On Some Steady-state Moving Boundary Problems in the Linear Theory of Viscoelasticity

Three steady-state moving boundary problems in the linear theoryof viscoelasticity are considered when the inertia terms aretaken into account. Attention is directed to the dimensionlessparameter = V/L where V is the speed of the boundary, is therelaxation time of the medium, and L is a length associatedwith the geometry of the problem. When is small the problemsare recognized as having a singular perturbation character andthe method of matched asymptotic expansions is used. The problemsare (i) a semi-infinite crack moving steadily in a clamped viscoelasticstrip, (ii) a finite length crack moving in an infinite viscoelasticmedium, and (iii) a steady rolling cylinder on a visco-elastichalf-space.