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The Riemann problem near a hyperbolic singularity

By E. Isaacson, D. Marchesin, B. Plohr and B. Temple


Abstract. The purpose of this paper is to classify the solutions of Riemann problems near a hyperbolic singularity in a nonlinear system of conservation laws. Hyperbolic singularities play the role in the theory of Riemann problems that rest points play in the theory of ordinary differential equations: Indeed, generically, only a finite number of structures can appear in a neighborhood of such a singularity. In this, the first of three papers, the program of classification is discussed in general and the simplest structure that occurs is characterized. Key words, nonlinear hyperbolic conservation laws, Riemann problems, hyperbolic singularities AMS(MOS) subject classifications

Topics: u, , x> o
Year: 1988
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