The Cauchy problem for a multidimensional linear
transport equation with discontinuous coefficient is investigated.
Provided the coefficient satisfies a one-sided Lipschitz condition,
existence, uniqueness and weak stability of solutions are obtained
for either the conservative backward problem or the advective
forward problem by duality.
Specific uniqueness criteria are introduced for the backward
conservation equation since weak solutions are not unique.
A main point is the introduction of a generalized flow in the sense of
partial differential equations, which is proved to have unique
jacobian determinant, even though it is itself nonunique.
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