Free Access
Volume 44, Number 1, January-February 2010
Page(s) 133 - 166
Published online 16 December 2009
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, Switzerland (2005).
  2. V.I. Arnold and B.A. Khesin,Topological methods in hydrodynamics, Applied Mathematical Sciences 125. Springer-Verlag, New York, USA (1998).
  3. L.A. Caffarelli, Allocation maps with general cost functions, in Partial differential equations and applications, P. Marcellini, G.G. Talenti and E. Vesintini Eds., Lecture Notes in Pure and Applied Mathematics 177, Marcel Dekker, Inc., New York, USA (1996) 29–35.
  4. G.-Q. Chen and D. Wang, The Cauchy problem for the Euler equations for compressible fluids, Handbook of mathematical fluid dynamics I. Elsevier, Amsterdam, North-Holland (2002) 421–543.
  5. C.M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws. J. Differential Equations 14 (1973) 202–212. [CrossRef] [MathSciNet]
  6. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet]
  7. W. Gangbo and M. Westdickenberg, Optimal transport for the system of isentropic Euler equations. Comm. Partial Diff. Eq. 34 (2009) 1041–1073. [CrossRef]
  8. E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd edition, Springer, Berlin, Germany (2000).
  9. D.D. Holm, J.E. Marsden and T.S. Ratiu, The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137 (1998) 1–81. [CrossRef] [MathSciNet]
  12. D. Kinderlehrer and N.J. Walkington, Approximation of parabolic equations using the Wasserstein metric. ESAIM: M2AN 33 (1999) 837–852. [CrossRef] [EDP Sciences]
  13. J.E. Marsden and M. West, Discrete mechanics and variational integrators. Acta Numer. 10 (2001) 357–514. [CrossRef] [MathSciNet]
  14. J. Nocedal and S.J. Wright, Numerical Optimization. Springer, New York, USA (1999).
  15. F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Diff. Eq. 26 (2001) 101–174. [CrossRef] [MathSciNet]
  16. J.L. Vázquez, Perspectives in nonlinear diffusion: between analysis, physics and geometry, in International Congress of Mathematicians I (2007) 609–634.
  17. C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics 58. American Mathematical Society, Providence, USA (2003).

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