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A kinetic formulation of multidimensional scalar conservation laws and related equations. (English) Zbl 0820.35094
A new formulation of multidimensional scalar conservation laws, which includes both the equation and the entropy criterion is presented. The formulation involves an additional variable called velocity by analogy. Among the applications of this formalism, some new compactness and regularity results for entropy solutions are given. This kinetic formulation is valid for more general classes of equations like equations involving nonlinear second-order terms.

MSC:
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
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