ON UNIQUENESS OF MEASURE-VALUED SOLUTIONS TO LIOUVILLE'S EQUATION OF HAMILTONIAN PDES

被引：2

作者：

Zied, Ammari ^{[1
]}

Quentin, Liard ^{[2
]}

机构：

[1] Univ Rennes 1, IRMAR, CNRS, UMR 6625, Campus Beaulieu, F-35042 Rennes, France

[2] Univ Paris 13, LAGA, CNRS, UMR 9345, Av JB Clement, F-93430 Villetaneuse, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 02期

关键词：

Continuity equation; method of characteristics; measure-valued solutions; nonlinear PDEs; NONLINEAR SCHRODINGER-EQUATION; CLASSICAL FIELD LIMIT; STATISTICAL-MECHANICS; CONTINUITY EQUATIONS; WIGNER MEASURES; WELL-POSEDNESS; VECTOR-FIELDS; QUANTUM; DYNAMICS; PROPAGATION;

D O I：

10.3934/dcds.2018032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Cauchy problem of classical Hamiltonian PDEs is recast into a Liouville's equation with measure-valued solutions. Then a uniqueness property for the latter equation is proved under some natural assumptions. Our result extends the method of characteristics to Hamiltonian systems with in finite degrees of freedom and it applies to a large variety of Hamiltonian PDEs (Hartree, Klein-Gordon, Schrodinger, Wave, Yukawa...). The main arguments in the proof are a projective point of view and a probabilistic representation of measure-valued solutions to continuity equations in finite dimension.

引用

页码：723 / 748

页数：26

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