Global Solutions in L^infinity for a System of Conservation Laws of Viscoelastic Materials with Memory

Abstract

We construct global solutions in L^∞ for the equations of motion or one-dimensional viscoelastic media, in Lagrangian coordinates, with arbitrarily large L^∞ initial data, via the vanishing viscosity method. A priori estimates for approximate solutions, with artificial viscosity, are derived through entropy inequalities. The convergence of the approximate solutions to a weak solution compatible with the entropy condition is demonstrated. This also establishes the compactness of the corresponding solution operators, which indicates that the memory effect does not affect the hyperbolic behavior.