Found 71 Documents (Results 1–71)
Wasserstein geometry and Ricci curvature bounds for Poisson spaces. (Géométrie de Wasserstein et minoration de la courbure de Ricci pour les espaces de Poisson.) (English. French summary) Zbl 07912281
Reviewer: Feng-Yu Wang (Tianjin)
From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows. (English) Zbl 07899597
Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances. (English) Zbl 1534.65091
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems. (English) Zbl 1533.65161
Gradient flows for probabilistic frame potentials in the Wasserstein space. (English) Zbl 1518.42045
An invitation to optimal transport. Wasserstein distances, and gradient flows. 2nd edition. (English) Zbl 1527.49001
EMS Textbooks in Mathematics. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-050-1/hbk; 978-3-98547-550-6/ebook). vi, 146 p. (2023).
Reviewer: Antonio Masiello (Bari)
An invariance principle for gradient flows in the space of probability measures. (English) Zbl 1511.35030
Reviewer: Debabrata Karmakar (Bangalore)
Data-driven gradient flows. (English) Zbl 1502.49031
Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems. (English) Zbl 07593593
Entropic regularization of nongradient systems. (English) Zbl 1500.35201
Reviewer: Nicolò De Ponti (Trieste)
Entropy, from Clausius to functional inequalities. (L’entropie, de Clausius aux inégalités fonctionnelles.) (French) Zbl 1486.35001
Weak topology and Opial property in Wasserstein spaces, with applications to gradient flows and proximal point algorithms of geodesically convex functionals. (English) Zbl 1484.60002
Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 32, No. 4, 725-750 (2021).
Lagrangian schemes for Wasserstein gradient flows. (English) Zbl 1473.65185
Bonito, Andrea (ed.) et al., Geometric partial differential equations. Part 2. Amsterdam: Elsevier/North Holland. Handbook of Numerical Analysis 22, 271-311 (2021).
An invitation to optimal transport, Wasserstein distances, and gradient flows. (English) Zbl 1472.49001
EMS Textbooks in Mathematics. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-010-5/hbk; 978-3-98547-510-0/ebook). vi, 136 p. (2021).
Reviewer: Jie Xiao (St. John’s)
Lectures on optimal transport. (English) Zbl 1485.49001
Unitext 130. La Matematica per il 3+2. Cham: Springer (ISBN 978-3-030-72161-9/pbk; 978-3-030-72162-6/ebook). ix, 250 p. (2021).
Reviewer: Nicolò De Ponti (Trieste)
A variational finite volume scheme for Wasserstein gradient flows. (English) Zbl 1452.49019
Reviewer: Sorin-Mihai Grad (Wien)
TPFA finite volume approximation of Wasserstein gradient flows. (English) Zbl 1454.65097
Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 193-201 (2020).
Bound preserving and energy dissipative schemes for porous medium equation. (English) Zbl 1436.65101
Gromov-Hausdorff limit of Wasserstein spaces on point clouds. (English) Zbl 1436.49017
Reviewer: Stepan Agop Tersian (Rousse)
Simulation of multiphase porous media flows with minimising movement and finite volume schemes. (English) Zbl 1425.76158
Rigorous theory of gradient flows and geodesic convexity with respect to geometric structure of Hellinger-Kantorovich-Wasserstein type on the space of finite Radon measures. (Russian. English summary) Zbl 1402.49041
Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance. (English) Zbl 1379.60089
Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 978-3-11-043926-7/hbk; 978-3-11-043041-7/ebook). Radon Series on Computational and Applied Mathematics 17, 400-416 (2017).
On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows. (English) Zbl 1379.35159
Bergounioux, Maïtine (ed.) et al., Topological optimization and optimal transport in the applied sciences. Berlin: De Gruyter (ISBN 978-3-11-043926-7/hbk; 978-3-11-043041-7/ebook). Radon Series on Computational and Applied Mathematics 17, 304-332 (2017).
Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions. (English) Zbl 1375.35552
Incompressible immiscible multiphase flows in porous media: a variational approach. (English) Zbl 1370.35230
The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion. (English) Zbl 1439.35296
Critical mass of degenerate Keller-Segel system with no-flux and Neumann boundary conditions. (English) Zbl 1364.35168
Long-time behavior of a fully discrete Lagrangian scheme for a family of fourth order equations. (English) Zbl 1355.65117
A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts. (English) Zbl 1361.35077
An augmented Lagrangian approach to Wasserstein gradient flows and applications. (English. French summary) Zbl 1354.49066
MSC:
49M30
49Q20
Generalized solutions of a kinetic granular media equation by a gradient flow approach. (English) Zbl 1339.35309
Periodic solutions for a 1D-model with nonlocal velocity via mass transport. (English) Zbl 1339.35237
Reviewer: Alain Brillard (Riedisheim)
Nonlocal interaction equations in environments with heterogeneities and boundaries. (English) Zbl 1327.35057
Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation. (English) Zbl 1321.49025
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D. (English) Zbl 1316.35077
Gradient flows in Wasserstein spaces and applications to crowd movement. (English) Zbl 1272.49098
Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 2009-2010, Exp. No. XXVII, 16 p. (2012).
From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach. (English) Zbl 1264.26011
Reviewer: Jacques Franchi (Strasbourg)
Measure valued solutions of sub-linear diffusion equations with a drift term. (English) Zbl 1267.35100
Gradient flows of the entropy for finite Markov chains. (English) Zbl 1237.60058
Reviewer: Stella Kapodistria (Eindhoven)
Some remarks on the equivalence between metric formulations of gradient flows. (English) Zbl 1217.49009
Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows. (English) Zbl 1200.35340
Reviewer: Adrian Muntean (Eindhoven)
A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. (English) Zbl 1203.35126
Reviewer: Giuseppe Buttazzo (Pisa)
Nonlinear mobility continuity equations and generalized displacement convexity. (English) Zbl 1225.49043
Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces. (English) Zbl 1178.35201
Reviewer: Vyacheslav I. Maksimov (Ekaterinburg)
Eulerian calculus for the displacement convexity in the Wasserstein distance. (English) Zbl 1166.58011
Reviewer: Dian K. Palagachev (Bari)
Steepest descent flows and applications to spaces of probability measures. (English) Zbl 1115.35012
Vázquez, Juan Luis (ed.) et al., Recent trends in partial differential equations. UIMP-RSME Santaló summer school, Santander, Spain, July 12–16, 2004. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 0-8218-3891-1/pbk). Contemporary Mathematics 409, 1-32 (2006).
Reviewer: Sabir R. Umarov (Albuquerque)
Convex functionals of probability measures and nonlinear diffusions on manifolds. (English) Zbl 1259.49074
Optimal transportation theory and geometric partial differential equations. (English) Zbl 1142.35001
Hill, James M. (ed.) et al., Applied mathematics entering the 21st century. Papers from the 5th international congress on industrial and applied mathematics (ICIAM 2003), Sydney, Australia, July 7–11, 2003. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-89871-559-0/hbk). Proceedings in Applied Mathematics 116, 37-47 (2004).
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