Mathematical analysis reveals that flows generated by scalar conservation laws are generically shift-differentiable, providing a new differentiation framework for functions of bounded variation.
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.
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Bressan et al. (1997) studied this question.
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