SOME NEW WELL-POSEDNESS RESULTS FOR CONTINUITY AND TRANSPORT EQUATIONS, AND APPLICATIONS TO THE CHROMATOGRAPHY SYSTEM

被引：40

作者：

Ambrosio, Luigi ^{[1
]}

Crippa, Gianluca ^{[2
]}

Figalli, Alessio ^{[3
]}

Spinolo, Laura V. ^{[4
]}

机构：

[1] Scuola Normale Super Pisa, I-56126 Pisa, Italy

[2] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy

[3] Ecole Polytech, Ctr Math Laurent Schwartz, F-91128 Palaiseau, France

[4] Scuola Normale Super Pisa, Coll Puteano, Ctr Giorgi, I-56126 Pisa, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2009年 / 41卷 / 05期

关键词：

continuity equation; chromatography system; BV functions; CONSERVATION-LAWS; HYPERBOLIC-SYSTEMS; CAUCHY-PROBLEM; VECTOR-FIELDS; SPACE DIMENSIONS; UNIQUENESS; STABILITY; BV; FLOW;

D O I：

10.1137/090754686

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1890 / 1920

页数：31

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