Shift-differentiabilitiy of the flow generated by a conservation law

Alberto Bressan; Graziano Guerra

doi:10.3934/dcds.1997.3.35

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1997, Volume 3, Issue 1: 35-58. Doi: 10.3934/dcds.1997.3.35

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Shift-differentiabilitiy of the flow generated by a conservation law

Alberto Bressan^1, and
Graziano Guerra²

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

Received: July 1996

Published: January 1997

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Abstract

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: 35L65.

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