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 functin $u$, 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.
Bressan, A., Guerra, G. (1997). Shift-differentiability of the flow generated by a conservation law. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 3(1), 35-58.
Shift-differentiability of the flow generated by a conservation law
GUERRA, GRAZIANO
1997
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 functin $u$, 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.
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