Lagrangian Representations for Linear and Nonlinear Transport

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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.

About the authors

Stefano Bianchini

S.I.S.S.A

Email: bianchin@sissa.it
via Bonomea 265, 34136 Trieste, Italy

Paolo Bonicatto

S.I.S.S.A

Email: paolo.bonicatto@sissa.it
via Bonomea 265, 34136 Trieste, Italy

Elio Marconi

S.I.S.S.A

Email: elio.marconi@sissa.it
via Bonomea 265, 34136 Trieste, Italy

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