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

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

2009-04-02

arxiv.org/abs/0904.0359v2

Mathematics

Analysis of PDEs

33 pages, minor changes

Scientific paper

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 x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension.

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