An overview on some results concerning the transport equation and its applications to conservation laws

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September 2010, 9(5): 1283-1293. doi: 10.3934/cpaa.2010.9.1283

An overview on some results concerning the transport equation and its applications to conservation laws

Gianluca Crippa ^1, and Laura V. Spinolo ^2,

1.	Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma
2.	Centro De Giorgi, Collegio Puteano, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56126 Pisa, Italy

Received August 2009 Revised September 2009 Published May 2010

Abstract
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We provide an informal overview on the theory of transport equa- tions with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.

Keywords: BV functions., Continuity equation, conservation laws.

Mathematics Subject Classification: 35F10, 35L6.

Citation: Gianluca Crippa, Laura V. Spinolo. An overview on some results concerning the transport equation and its applications to conservation laws. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1283-1293. doi: 10.3934/cpaa.2010.9.1283

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