The Riemann Problem for the System u(t) + Sigma(x) = O and (Sigma - f(u))(t) + (sigma - muf(u)) = o.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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
- Numerical Mathematics