HAMILTON-JACOBI EQUATIONS IN THE WASSERSTEIN SPACE

被引：0

作者：

Gangbo, Wilfrid ^{[1
]}

Truyen Nguyen ^{[2
]}

Tudorascu, Adrian ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Akron, Dept Theoret & Appl Math, Akron, OH 44325 USA

来源：

METHODS AND APPLICATIONS OF ANALYSIS | 2008年 / 15卷 / 02期

关键词：

Hamilton-Jacobi equations in infinite dimension; viscosity solutions; mass transfer; Wasserstein metric;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the link between HJE in the Wasserstein space and Fluid Mechanics, in the last part of the paper we focus on a special Hamiltonian. The characteristics for these HJE are solutions of physical systems in finite dimensional spaces.

引用

页码：155 / 183

页数：29

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