Weak singularities in the multi-dimensional Riemann Problem
Seminar Room 2, Newton Institute Gatehouse
AbstractThe Riemann Problem consists in looking at self-similar solutions of first order systems of conservation laws, like compressible gas dynamics. In one space dimension, it is solved by shocks and rarefaction waves. Both kinds have generalizations in several space variables, where the wave fronts are free boundaries. We study the rarefaction case in detail and show that the gradient jump at the front can be calculated explicitly when the outer state is constant. This jump depends upon the dimension $d$ and vanishes when $d=3$. This is a joint work with H. Freisthueler (Univ. Konstanz)
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