Approximation of parabolic equations using the Wasserstein metric
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 837-852.
@article{M2AN_1999__33_4_837_0,
     author = {Kinderlehrer, David and Walkington, Noel J.},
     title = {Approximation of parabolic equations using the {Wasserstein} metric},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {837--852},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4},
     year = {1999},
     mrnumber = {1726488},
     zbl = {0936.65121},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_4_837_0/}
}
TY  - JOUR
AU  - Kinderlehrer, David
AU  - Walkington, Noel J.
TI  - Approximation of parabolic equations using the Wasserstein metric
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 837
EP  - 852
VL  - 33
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_4_837_0/
LA  - en
ID  - M2AN_1999__33_4_837_0
ER  - 
%0 Journal Article
%A Kinderlehrer, David
%A Walkington, Noel J.
%T Approximation of parabolic equations using the Wasserstein metric
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 837-852
%V 33
%N 4
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_1999__33_4_837_0/
%G en
%F M2AN_1999__33_4_837_0
Kinderlehrer, David; Walkington, Noel J. Approximation of parabolic equations using the Wasserstein metric. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 837-852. http://www.numdam.org/item/M2AN_1999__33_4_837_0/

[1] J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Preprint (1998). | Zbl

[2] J. Benamou and Y. Brenier, Weak existence for the semigeostrophic equations formulated as a coupled Monge-Ampere transport problem. SIAM J. AppL Math. 58 (1998) 1450-1461. | MR | Zbl

[3] Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44 (1991)375-417. | MR | Zbl

[4] P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation. Cambridge University Press, Cambridge (1988). | MR | Zbl

[5] W.E. and F. Otto, Thermodynamically driven incompressible fluid mixtures. J. Chem. Phys. 107 (1998) 10177-10184. | Zbl

[6] M. Frechet, Sur la distance de deux lois de probabilité. C.R. Acad. Sci. 244 (1957) 689-692. | MR | Zbl

[7] W. Gangbo and A. Sweich, Optimal maps for the multidimensional Monge-Kantorovich problem. CPAM 51 (1998) 23-45. | MR | Zbl

[8] W. Gango and R.J. Mccann, The geometry of optimal transportation. Acta Math, 177 (1996) 113-161. | MR | Zbl

[9] R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck équation. SIAM J. Math. Anal. 29 (1998) 1-17. | MR | Zbl

[10] R. Jordan, D. Kinderlehrer and F. Otto, Dynamics of the Fokker-Planck equation. Phase Transitions (to appear).

[11] E.H. Lieb and M. Loss, Analysis, Vol. 14 of Graduate Studies in Mathematics. AMS (1997). | MR | Zbl

[12] F. Otto, Dynamics of labyrinthine pattern formation in magnetic fluids. Arch. Rational Mech. Anal. 141 (1998) 63-103. | MR | Zbl

[13] N.G. Van Kampen, Stochastic Processes in Physics and Chemistry. North-Holland (1981). | MR | Zbl