Displaying similar documents to “Transport equation and Cauchy problem for B V vector fields and applications”

Some remarks on multidimensional systems of conservation laws

Alberto Bressan (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.

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

Francois Bouchut, Francois James, Simona Mancini (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...

Transport equations with partially B V velocities

Nicolas Lerner (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem ∂ t u + X u = f , u | t = 0 = g , where X is the vector fieldwith a boundedness condition on the divergence of each vector field a 1 , a 2 . This model was studied in the paper [LL] with a W 1 , 1 regularity assumption replacing our B V hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the...