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Preprint 2009-015

Some new well-posedness results for continuity and transport equations, and applications to the chromatography system

Luigi Ambrosio, Gianluca Crippa, Alessio Figalli and Laura V. Spinolo

Abstract: We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k k chromatography system of conservation laws and to the k k Keyfitz and Kranzer system, both in one space dimension.

Paper:
Available as PDF (392 Kbytes).
Author(s):
Luigi Ambrosio
Gianluca Crippa
Alessio Figalli
Laura V. Spinolo
Publishing information:
The paper is also on arXiv.
Comments:
Updated 2009-10-01.
Submitted by:
; 2009-04-03.