Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient
Francois Bouchut, Francois James, and Simona Mancini
The Cauchy problem for a multidimensional linear
transport equation with discontinuous coefficient
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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- Francois Bouchut,
- Francois James
- Simona Mancini
- Publishing information:
- Submitted by:
May 18 2004.
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