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In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative measures endowed with an optimal transport-growth metric.
Strong convergence results related to strict convexity
Augusto Visintin · 1984
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The variational formulation of the Fokker–Planck equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
Felix Otto · 1998
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Variatonal formulation for the lubrication approximation of the Hele-Shaw flow
Lorenzo Giacomelli and Felix Otto · 2001
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Gradient flows: in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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A new transportation distance between non-negative measures, with applications to gradients flows with dirichlet boundary conditions
Alessio Figalli and Nicola Gigli · 2010
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A macroscopic crowd motion model of gradient flow type
Bertrand Maury, Aude Roudneff-Chupin, and Filippo Santambrogio · 2010
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Handling congestion in crowd motion modeling
Bertrand Maury, Aude Roudneff-Chupin, Filippo Santambrogio, and Juliette Venel · 2011
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Nonlinear Perron-Frobenius Theory
Bas Lemmens and Roger Nussbaum · 2012
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From the schrödinger problem to the monge–kantorovich problem
Christian Léonard · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Gradient structures and geodesic convexity for reaction–diffusion systems
Matthias Liero and Alexander Mielke · 2013
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The Hele-Shaw asymptotics for mechanical models of tumor growth
Benoît Perthame, Fernando Quirós, and Juan Luis Vázquez · 2014
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Iterative bregman projections for regularized transportation problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré · 2015
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Unbalanced optimal transport: geometry and kantorovich formulation
Lénaïc Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2015
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An interpolating distance between optimal transport and fisher-rao
Lénaïc Chizat, Bernhard Schmitzer, Gabriel Peyré, and François-Xavier Vialard · 2015
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Entropic approximation of Wasserstein gradient flows
Gabriel Peyré · 2015
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Scaling algorithms for unbalanced transport problems
Lénaïc Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2016
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Bv estimates in optimal transportation and applications
Guido De Philippis, Alpár Richárd Mészáros, Filippo Santambrogio, and Bozhidar Velichkov · 2016
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Uniqueness issues for evolution equations with density constraints
Simone Di Marino and Alpár Richárd Mészáros · 2016
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A jko splitting scheme for kantorovich-fisher-rao gradient flows
Thomas Galloüet and Leonard Monsaingeon · 2016
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Stanislav Kondratyev, Léonard Monsaingeon, and Dmitry Vorotnikov · 2015
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Matthias Liero, Alexander Mielke, and Giuseppe Savaré · 2015
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Matthias Liero, Alexander Mielke, and Giuseppe Savaré · 2015
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Pressureless euler equations with maximal density constraint: a time-splitting scheme
Bertrand Maury and Anthony Preux · 2015
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A Hele-Shaw problem for tumor growth
Antoine Mellet, Benoît Perthame, and Fernando Quiros · 2015
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On geodesic λ \lambda -convexity with respect to the Hellinger-Kantorovich distance
Matthias Liero, Alexander Mielke, and Giuseppe Savaré
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A fitness-driven cross-diffusion system from population dynamics as a gradient flow
Stanislav Kondratyev, Léonard Monsaingeon, and Dmitry Vorotnikov · 2016
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Stabilized sparse scaling algorithms for entropy regularized transport problems
Bernhard Schmitzer · 2016
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Convergence of entropic schemes for optimal transport and gradient flows
G. Carlier, V. Duval, G. Peyré, and B. Schmitzer · 2017
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An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
Thomas Gallouët, Maxime Laborde, and Leonard Monsaingeon · 2017
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{ \{ Euclidean, metric, and Wasserstein } \} gradient flows: an overview
Filippo Santambrogio · 2017
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