Hamilton-Jacobi Equations in the Wasserstein Space
Gangbo, Wilfrid ; Nguyen, Truyen ; Tudorascu, Adrian
Methods Appl. Anal., Tome 15 (2008) no. 1, p. 155-184 / Harvested from Project Euclid
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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.
Publié le : 2008-06-15
Classification:  Hamilton-Jacobi equations in infinite dimension,  viscosity solutions,  mass transfer,  Wasserstein metric,  49J40,  82C40,  47J25 
@article{1234536492,
     author = {Gangbo, Wilfrid and Nguyen, Truyen and Tudorascu, Adrian},
     title = {Hamilton-Jacobi Equations in the Wasserstein Space},
     journal = {Methods Appl. Anal.},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 155-184},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1234536492}
}

Gangbo, Wilfrid; Nguyen, Truyen; Tudorascu, Adrian. Hamilton-Jacobi Equations in the Wasserstein Space. Methods Appl. Anal., Tome 15 (2008) no. 1, pp.  155-184. http://gdmltest.u-ga.fr/item/1234536492/