Mathematics – Analysis of PDEs
Scientific paper
2004-03-23
Annali della Scuola Normale Superiore di Pisa, Cl. Sci. (5) IV (2005) 1-25
Mathematics
Analysis of PDEs
19-03-2004
Scientific paper
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.
Bouchut Francois
James Francois
Mancini Simona
No associations
LandOfFree
Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-89673