Skip to Main content Skip to Navigation
Journal articles

Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient

Abstract : 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.
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00001351
Contributor : Francois James <>
Submitted on : Tuesday, March 23, 2004 - 8:48:57 PM
Last modification on : Tuesday, August 4, 2020 - 3:44:20 AM
Document(s) archivé(s) le : Monday, March 29, 2010 - 5:35:16 PM

Identifiers

Citation

François Bouchut, Francois James, Simona Mancini. Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2005, 4 (1), pp.1-25. ⟨10.2422/2036-2145.2005.1.01⟩. ⟨hal-00001351⟩

Share

Metrics

Record views

633

Files downloads

145