title: Focusing of noncircular self-similar shock waves.
abstract: We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.
authors.affiliation: Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, Minneapolis, Minnesota 55455, USA.
authors.forename: S I
authors.initials: SI
authors.lastname: Betelu
authors.forename: D G
authors.initials: DG
authors.lastname: Aronson