Elastic as Limit of Viscoelastic Response, in a Context of Self-Similar Viscous Limits

We study the equations of one-dimensional isothermal elastic response as the small viscosity limit of the equations of viscoelasticity, in a context of self-similar viscous limits for Riemann data. No size restrictions on the data or genuine-nonlinearity assumptions are imposed. The limiting procedure is justified and a solution of the Riemann problem for the equations of elasticity is obtained. The emerging solution is composed of two wave fans, each consisting of rarefactions, shocks and contact discontinuities, separated by constant states. At shocks the self-similar viscous solution has the internal structure of traveling waves, and an admissibility criterion identified by Wendroff [W] is fullfilled.