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 CMFD, 2017, Volume 63, Issue 3, Pages 418–436 (Mi cmfd327)

Lagrangian representations for linear and nonlinear transport

S. Bianchini, P. Bonicatto, E. Marconi

S.I.S.S.A., via Bonomea 265, 34136 Trieste, Italy

Abstract: In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

DOI: https://doi.org/10.22363/2413-3639-2017-63-3-418-436

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UDC: 517.952

Citation: S. Bianchini, P. Bonicatto, E. Marconi, “Lagrangian representations for linear and nonlinear transport”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 418–436

Citation in format AMSBIB
\Bibitem{BiaBonMar17} \by S.~Bianchini, P.~Bonicatto, E.~Marconi \paper Lagrangian representations for linear and nonlinear transport \inbook Differential and functional differential equations \serial CMFD \yr 2017 \vol 63 \issue 3 \pages 418--436 \publ Peoples' Friendship University of Russia \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd327} \crossref{https://doi.org/10.22363/2413-3639-2017-63-3-418-436}