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June 2008 Hamilton-Jacobi Equations in the Wasserstein Space
Wilfrid Gangbo, Truyen Nguyen, Adrian Tudorascu
Methods Appl. Anal. 15(2): 155-184 (June 2008).

Abstract

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.

Citation

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Wilfrid Gangbo. Truyen Nguyen. Adrian Tudorascu. "Hamilton-Jacobi Equations in the Wasserstein Space." Methods Appl. Anal. 15 (2) 155 - 184, June 2008.

Information

Published: June 2008
First available in Project Euclid: 13 February 2009

zbMATH: 1171.49308
MathSciNet: MR2481677

Subjects:
Primary: 47J25, 49J40, 82C40

Rights: Copyright © 2008 International Press of Boston

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Vol.15 • No. 2 • June 2008
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