An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
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[1] Jonathan Zinsl. Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations , 2014, 1412.3266.
[2] B. Perthame,et al. The Hele–Shaw Asymptotics for Mechanical Models of Tumor Growth , 2013, Archive for Rational Mechanics and Analysis.
[3] Simone Di Marino,et al. A tumor growth model of Hele-Shaw type as a gradient flow , 2017, ESAIM: Control, Optimisation and Calculus of Variations.
[4] Felix Otto,et al. Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean‐Field Theory , 1998 .
[5] Alexander Mielke,et al. Optimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves , 2015, SIAM J. Math. Anal..
[6] Gershon Wolansky,et al. Optimal Transport , 2021 .
[7] F. Santambrogio,et al. BV Estimates in Optimal Transportation and Applications , 2015, 1503.06389.
[8] Thomas O. Gallouët,et al. A JKO Splitting Scheme for Kantorovich-Fisher-Rao Gradient Flows , 2016, SIAM J. Math. Anal..
[9] Xiang Xu,et al. A Wasserstein gradient flow approach to Poisson−Nernst−Planck equations , 2015, 1501.04437.
[10] C. Villani. Topics in Optimal Transportation , 2003 .
[11] F. Fleißner. Γ-convergence and relaxations for gradient flows in metric spaces: a minimizing movement approach , 2016, ESAIM: Control, Optimisation and Calculus of Variations.
[12] F. Santambrogio. Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , 2015 .
[13] S. Serfaty,et al. Gamma‐convergence of gradient flows with applications to Ginzburg‐Landau , 2004 .
[14] Riccarda Rossi,et al. Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces , 2003 .
[15] Lénaïc Chizat,et al. Scaling Algorithms for Unbalanced Transport Problems , 2016, 1607.05816.
[16] G. Peyré,et al. Unbalanced Optimal Transport: Geometry and Kantorovich Formulation , 2015 .
[17] A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts , 2016, 1606.04793.
[18] W. Gangbo,et al. The geometry of optimal transportation , 1996 .
[19] F. Otto. THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION , 2001 .
[20] Jean-David Benamou,et al. An augmented Lagrangian approach to Wasserstein gradient flows and applications , 2016 .
[21] Giuseppe Savaré,et al. Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures , 2015, 1508.07941.
[22] Bertrand Maury,et al. Handling congestion in crowd motion modeling , 2011, Networks Heterog. Media.
[23] Matthias Liero,et al. Gradient structures and geodesic convexity for reaction–diffusion systems , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[24] François-Xavier Vialard,et al. An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics , 2010, Foundations of Computational Mathematics.
[25] Felix Otto,et al. Doubly Degenerate Diffusion Equations as Steepest Descent , 1996 .
[26] L. Ambrosio,et al. Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .
[27] Nicola Gigli,et al. A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions , 2010 .
[28] A. Tudorascu,et al. Variational Principle for General Diffusion Problems , 2004 .
[29] M. Golinski,et al. Mathematical Biology , 2005 .
[30] M. Laborde. On some non linear evolution systems which are perturbations of Wasserstein gradient flows , 2015, 1506.00126.
[31] B. Piccoli,et al. Generalized Wasserstein Distance and its Application to Transport Equations with Source , 2012, 1206.3219.
[32] Andrea Braides. Γ-convergence for beginners , 2002 .
[33] B. Perthame,et al. Traveling wave solution of the Hele–Shaw model of tumor growth with nutrient , 2014, 1401.3649.
[34] B. Perthame. Transport Equations in Biology , 2006 .
[35] Ronald F. Gariepy. FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs) , 2001 .
[36] S. Kondratyev,et al. A new optimal transport distance on the space of finite Radon measures , 2015, Advances in Differential Equations.
[37] D. Kinderlehrer,et al. THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .
[38] Dmitry Vorotnikov,et al. A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow , 2016, 1603.06431.
[39] Daniel Matthes,et al. Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics , 2012, 1201.2367.
[40] Inwon C. Kim,et al. Quasi-static evolution and congested crowd transport , 2013, 1304.3072.
[41] Marco Di Francesco,et al. Measure solutions for non-local interaction PDEs with two species , 2013 .
[42] J. Carrillo,et al. Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations , 2011 .
[43] Yann Brenier,et al. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , 2000, Numerische Mathematik.
[44] M. Pierre. Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey , 2010 .
[45] Filippo Santambrogio,et al. Optimal Transport for Applied Mathematicians , 2015 .
[46] J. Vázquez. The Porous Medium Equation: Mathematical Theory , 2006 .
[47] M. Agueh. Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory. , 2002, math/0309410.
[48] R. McCann,et al. A Family of Nonlinear Fourth Order Equations of Gradient Flow Type , 2009, 0901.0540.