Well-posedness theory for hyperbolic conservation laws

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1553-1586
Journal / PublicationCommunications on Pure and Applied Mathematics
Issue number12
Publication statusPublished - Dec 1999


The paper presents a well-posedness theory for the initial value problem for a general system of hyperbolic conservation laws. We will start with the refinement of Glimm's existence theory and discuss the principle of nonlinear superposition through wave tracing. Our main goal is to introduce a nonlinear functional for two solutions with the property that it is equivalent to the L1(x) distance between the two solutions and is time-decreasing. Moreover, the functional is constructed explicitly in terms of the wave patterns of the solutions through the nonlinear superposition. It consists of a linear term measuring the L1(x) distance, a quadratic term measuring the coupling of waves and distance, and a generalized entropy functional. © 1999 John Wiley & Sons, Inc.