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 rest rictions on the data or genuine-nonlinearity assumptions are imposed. The limiting procedure is justified and a solution of the Riemann prob lem 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 travel ing waves, and an admissibility criterion identified by Wendroff [W] i s fullfilled. (C) 1995 Academic Press, Inc.