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A kinetic formulation of multidimensional scalar conservation laws and related equations


Authors: P.-L. Lions, B. Perthame and E. Tadmor
Journal: J. Amer. Math. Soc. 7 (1994), 169-191
MSC: Primary 35L65; Secondary 35K65
DOI: https://doi.org/10.1090/S0894-0347-1994-1201239-3
MathSciNet review: 1201239
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Abstract: We present a new formulation of multidimensional scalar conservation laws, which includes both the equation and the entropy criterion. This formulation is a kinetic one involving an additional variable called velocity by analogy. We also give some applications of this formulation to new compactness and regularity results for entropy solutions based upon the velocity-averaging lemmas. Finally, we show that this kinetic formulation is in fact valid and meaningful for more general classes of equations like equations involving nonlinear second-order terms.


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Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1994-1201239-3
Keywords: Scalar multidimensional conservation laws, entropy solutions, kinetic formulation, pseudo-maxwellian, velocity averaging, compactness, oscillations, genuine nonlinearity, regularity results, degenerate nonlinear parabolic equations
Article copyright: © Copyright 1994 American Mathematical Society