Lagrangian schemes for Wasserstein gradient flows (Q2235781)

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Language	Label	Description	Also known as
English	Lagrangian schemes for Wasserstein gradient flows	scientific article

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scholarly article

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Lagrangian schemes for Wasserstein gradient flows (English)

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zbMATH Open document ID

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10.1016/bs.hna.2020.10.002

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Marie-Therese Wolfram

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José Antonio Carrillo

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publication date

21 October 2021

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full work available at URL

https://arxiv.org/abs/2003.03803

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

Wasserstein gradient flows

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minimizing movement scheme

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Lagrangian discretization

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MaRDI profile type

MaRDI publication profile

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Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations

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Stability of flows associated to gradient vector fields and convergence of iterated transport maps

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On maps with given Jacobians involving the heat equation

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Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient-flow structure

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Dimensionality of local minimizers of the interaction energy

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Nonlocal interactions by repulsive-attractive potentials: radial ins/stability

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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

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An augmented Lagrangian approach to Wasserstein gradient flows and applications

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Discretization of functionals involving the Monge-Ampère operator

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Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

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Characterization of Radially Symmetric Finite Time Blowup in Multidimensional Aggregation Equations

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Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model

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Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model

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Polar factorization and monotone rearrangement of vector‐valued functions

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Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms

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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

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Contractions in the 2-Wasserstein length space and thermalization of granular media

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Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

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Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

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A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes

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Mean-field limit for collective behavior models with sharp sensitivity regions

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Structure preserving schemes for the continuum Kuramoto model: phase transitions

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A blob method for diffusion

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Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits

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On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift

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A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

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Optimal critical mass in the two dimensional Keller-Segel model in \(R^2\)

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Diffeomorphisms and Nonlinear Heat Flows

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Diffusion-based method for producing density-equalizing maps

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The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation

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Identification of Asymptotic Decay to Self-Similarity for One-Dimensional Filtration Equations

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Lagrangian Numerical Approximations to One‐Dimensional Convolution‐Diffusion Equations

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Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$

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A review of the mean field limits for Vlasov equations

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The Variational Formulation of the Fokker--Planck Equation

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A Fully Discrete Variational Scheme for Solving Nonlinear Fokker--Planck Equations in Multiple Space Dimensions

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Convergence of a Newton algorithm for semi-discrete optimal transport

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Lagrangian Discretization of Crowd Motion and Linear Diffusion

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Second-order in time schemes for gradient flows in Wasserstein and geodesic metric spaces

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Long-time asymptotics of kinetic models of granular flows

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Computations of optimal transport distance with Fisher information regularization

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Fisher information regularization schemes for Wasserstein gradient flows

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Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation

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A convergent Lagrangian discretization for a nonlinear fourth-order equation

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A variational formulation of the BDF2 method for metric gradient flows

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Convergent Lagrangian Discretization for Drift-Diffusion with Nonlocal Aggregation

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A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

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A convexity principle for interacting gases

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On the Volume Elements on a Manifold

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Long-time behavior of a fully discrete Lagrangian scheme for a family of fourth order equations

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14. Convergence of a fully discrete variational scheme for a thin-film equation

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Lubrication approximation with prescribed nonzero contact anggle

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THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION

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Optimal Transport with Proximal Splitting

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Computational Optimal Transport: With Applications to Data Science

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A BDF2-approach for the non-linear Fokker-Planck equation

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Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling

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One-dimensional kinetic models of granular flows

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Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations

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