Regularity of a scalar Riemann problem in two space dimensions (original) (raw)

Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 1993

Abstract

ABSTRACT For the one-dimensional scalar nonconvex conservation law u t +f(u) x =0 let f ''' (u) have finitely many changes of sign. We show that if the initial data consists of finitely many constant states, the solution will be piecewise smooth with finitely many shock curves. Hence the same holds true for two-dimensional Riemann problems for the scalar equation u t +f(u) x +f(u) y =0.

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