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January  1997, 3(1): 35-58. doi: 10.3934/dcds.1997.3.35

Shift-differentiabilitiy of the flow generated by a conservation law

Alberto Bressan 1, and  Graziano Guerra 2,

1. 

S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste
2. 

Dipartimento di Scienze dell'Ambeinte e del Territorio, Via L. Emanueli, 15 Bicocca, 20126 Milano, Italy

Received  July 1996 Published  October 1996

The paper introduces a notion of "shift-differentials" for maps with values in the space BV. These differentials describe first order variations of a given function $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition.
Mathematics Subject Classification: 35L6.
Citation: Alberto Bressan, Graziano Guerra. Shift-differentiabilitiy of the flow generated by a conservation law. Discrete & Continuous Dynamical Systems, 1997, 3 (1) : 35-58. doi: 10.3934/dcds.1997.3.35
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