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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A kinetic formulation of multidimensional scalar conservation laws and related equations
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by P.-L. Lions, B. Perthame and E. Tadmor PDF
J. Amer. Math. Soc. 7 (1994), 169-191 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • 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