WAVE INTERACTIONS AND VARIATION ESTIMATES FOR SELF-SIMILAR ZERO-VISCOSITY LIMITS IN SYSTEMS OF CONSERVATION-LAWS

We consider the problem of self-similar zero-viscosity limits for syst ems of N conservation laws. First, we give general conditions so that the resulting boundary-value problem admits solutions. The obtained ex istence theory covers a large class of systems, in particular the clas s of symmetric hyperbolic systems. Second, we show that if the system is strictly hyperbolic and the Riemann data are sufficiently close, th en the resulting family of solutions is of uniformly bounded variation and oscillation. Third, we construct solutions of the Riemann problem via self-similar zero-viscosity limits and study the structure of the emerging solution and the relation of self-similar zero-viscosity lim its and shock profiles. The emerging solution consists of N wave fans separated by constant states. Each wave fan is associated with one of the characteristic fields and consists of a rarefaction, a shock, or a n alternating sequence of shocks and rarefactions so that each shock a djacent to a rarefaction on one side is a contact discontinuity on tha t side. At shocks, the solutions of the self-similar zero-viscosity pr oblem have the internal structure of a traveling wave.