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Seminari di Equazioni Differenziali e Applicazioni: Initial-boundary value problems for transport equations with rough coefficients

Giovedì 16 Gennaio 2014, ore 12:15 - Aula 2BC30 - Laura Spinolo

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Giovedì 16 gennaio 2014 alle ore 12:15 in aula 2BC30, Laura Spinolo (IMATI-CNR, Pavia) terrà un seminario dal titolo "Initial-boundary value problems for transport equations with rough coefficients".

Abstract
The analysis of transport and continuity equations with weakly differentiable coefficients has recently received considerable attention. In particular, the fundamental papers by Di Perna and Lions and by Ambrosio establish existence and uniqueness of solutions of the Cauchy problem for continuity equations with Sobolev and BV (bounded total variation) coefficients, respectively. This analysis has important applications to the study of several nonlinear partial differential equations, like hyperbolic systems of conservation laws in several space dimensions.
In this seminar I will discuss recent results establishing existence and uniqueness of solutions of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. I will also exhibit some new counter-examples showing that, as soon as the BV regularity deteriorates at the domain boundary, uniqueness is in general violated.
The seminar will be based on joint works with G. Crippa and C. Donadello.

Rif. Int. M. Bardi, C. Marchi, F. Ancona.

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