Project A8: Variational structures for evolution equations, optimal transport, and synthetic curvature
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Summary:
One major focus of this project are gradient flows and other variational structures for evolutions in spaces of probability measures. We aim to identify such structures based on tailored geometries for large classes of PDEs and to exploit them in the analysis of singular limits and long-term behavior. Special emphasis will be put on optimal transport and evolutionary PDEs on networks. A second major focus is to push forward the analysis and geometry on singular spaces with synthetic bounds on the curvature.
Recent Preprints:
25035
Matthias Erbar, Zihui He PDF
Passing to the limit in fuzzy Boltzmann equations
Project:
A8
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Passing to the limit in fuzzy Boltzmann equations
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25030
Ehsan Abedi PDF
Fractional Sobolev paths on Wasserstein spaces and their energy-minimizing particle representations
Project:
A8
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Fractional Sobolev paths on Wasserstein spaces and their energy-minimizing particle representations
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25029
Ehsan Abedi PDF
Fractional Sobolev processes on Wasserstein spaces and their energy-minimizing particle representations with applications
Project:
A8
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Fractional Sobolev processes on Wasserstein spaces and their energy-minimizing particle representations with applications
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25028
Manh Hong Duong, Zihui He PDF
On a fuzzy Landau Equation: Part I. A variational approach
Project:
A8
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On a fuzzy Landau Equation: Part I. A variational approach
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24125
Gabriele Grillo, Giulia Meglioli, Fabio Punzo PDF
Blow-up and global existence for semilinear parabolic equations on infinite graphs
Project:
A8
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Blow-up and global existence for semilinear parabolic equations on infinite graphs
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24123
Matthias Erbar, Giulia Meglioli PDF
Gradient flow for a class of diffusion equations with dirichlet boundary data
Project:
A8
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Gradient flow for a class of diffusion equations with dirichlet boundary data
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24122
Giulia Meglioli PDF
On the uniqueness for the heat equation with density on infinite graphs
Project:
A8
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On the uniqueness for the heat equation with density on infinite graphs
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24029
Matthias Erbar, Zihui He PDF
A variational approach to a fuzzy Boltzmann equation
Project:
A8
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A variational approach to a fuzzy Boltzmann equation
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23121
Martin Burger, Matthias Erbar, Franca Hoffmann, Daniel Matthes, André Schlichting PDF
Covariance-modulated optimal transport and gradient flows
Project:
A8
Published: Archive for Rational Mechanics and Analysis 249 (2024), Article number 7
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Covariance-modulated optimal transport and gradient flows
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23117
Jorge Justiniano, Martin Rumpf, Matthias Erbar PDF
Approximation of splines in Wasserstein spaces
Project:
A8
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Approximation of splines in Wasserstein spaces
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All Publications of this Project
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