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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

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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