The Riemann Problem for the System u(t) + Sigma(x) = O and (Sigma - f(u))(t) + (sigma - muf(u)) = o

摘要

In this paper we study the Riemann Problem for a system of conservation laws which exhibit internal friction similar to that seen in viscoelastic solids of the maxwell type. The solutions we obtain have a single shock and a single contact discontinuity and off of these singular curves they are smooth. The results we obtain are two fold. First we show this problem is globally solvable in time; this requires precise a-priori estimates for the solution off of the singular curves. Secondly, we obtain asymptotic or large time information about the solution which guarantees that in a weak sense it converges to special traveling wave solutions of the equations with compatible data. (Author)