Excerpt from The Scalar Riemann Problem in Two Spatial Dimensions: Piecewise Smoothness of Solutions and Its Breakdown

The generalizations of the 1-dimensional Riemann problem to allow multiple jumps and resuicted smooth variation in the initial data are presented in 2 and 3. In §4, the two dimensional Riemann problem is defined and a suffio'ency condition for piecewise smooth solutions obtained.

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