Search results for Differential and integral equations, dynamical systems and control theory

2 - Discrete Transport Problems
from Part I - The Kantorovich Problem
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 14-34
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Summary

Pedagogical description of the Kantorovich theory in the discrete setting.

Epigraph
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

Published online:

02 November 2023

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16 November 2023, pp v-vi
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Index
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 294-296
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14 - The Euler Equations and Isochoric Projections
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 164-173
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Summary

Euler equations as geodesics equation and Brenier theorem as the associated projection theorem.

15 - Action Minimization, Eulerian Velocities, and Otto's Calculus
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

Published online:

02 November 2023

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16 November 2023, pp 174-192
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Summary

Curves of measures in the Wasserstein space and the Brenier–Benamou formula.

Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 95-96
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5 - First Order Differentiability of Convex Functions
from Part II - Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 67-72
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Summary

Fine first-order differentiability properties of convex functions.

Preface
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp xiii-xviii
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13 - The Fokker–Planck Equation in the Wasserstein Space
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 139-163
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Summary

Minimizing movement scheme for the Fokker–Planck equation in the Wasserstein space (Jordan–Kinderlehrer–Otto theorem).

18 - Solution to the Monge Problem with Linear Cost
from Part IV - Solution of the Monge Problem with Linear Cost: The Sudakov Theorem
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 216-246
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Summary

Solution of the Monge problem with linear cost, Sudakov maps.

Part II - Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 57-58
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9 - Isoperimetric and Sobolev Inequalities in Sharp Form
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 97-103
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Summary

Applications of Brenier maps to isoperimetric and Sobolev inequalities.

References
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

Published online:

02 November 2023

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16 November 2023, pp 288-293
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Part I - The Kantorovich Problem
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 1-2
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Dedication
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp vii-viii
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Frontmatter
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp i-iv
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Appendix A - Radon Measures on Rn and Related Topics
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

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02 November 2023

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16 November 2023, pp 268-280
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10 - Displacement Convexity and Equilibrium of Gases
from Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

Published online:

02 November 2023

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16 November 2023, pp 104-117
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Summary

Brenier maps and McCann's displacement interpolation.

Trend to equilibrium solution for the discrete Safronov–Dubovskiĭ aggregation equation with forcing
Part of
Arijit Das, Jitraj Saha
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 155 / Issue 3 / June 2025

Published online by Cambridge University Press:

16 November 2023, pp. 869-892

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June 2025
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We consider the discrete Safronov-Dubovskiĭ aggregation equation associated with the physical condition, where particle injection and extraction take place in the dynamical system. In application, this model is used to describe the aggregation of particle-monomers in combination with sedimentation of particle-clusters. More precisely, we prove well-posedness of the considered model for a large class of aggregation kernel with source and efflux coefficients. Furthermore, over a long time period, we prove that the dynamical model attains a unique equilibrium solution with an exponential rate under a suitable condition on the forcing coefficient.

Contents
Francesco Maggi, University of Texas, Austin
Book:

Optimal Mass Transport on Euclidean Spaces

Published online:

02 November 2023

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16 November 2023, pp ix-xii
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28888 results in Differential and integral equations, dynamical systems and control theory

2 - Discrete Transport Problems

Summary

Epigraph

Index

14 - The Euler Equations and Isochoric Projections

Summary

15 - Action Minimization, Eulerian Velocities, and Otto's Calculus

Summary

Part III - Applications to PDE and the Calculus of Variations and the Wasserstein Space

5 - First Order Differentiability of Convex Functions

Summary

Preface

13 - The Fokker–Planck Equation in the Wasserstein Space

Summary

18 - Solution to the Monge Problem with Linear Cost

Summary

Part II - Solution of the Monge Problem with Quadratic Cost: The Brenier–McCann Theorem

9 - Isoperimetric and Sobolev Inequalities in Sharp Form

Summary

References

Part I - The Kantorovich Problem

Dedication

Frontmatter

Appendix A - Radon Measures on Rn and Related Topics

10 - Displacement Convexity and Equilibrium of Gases

Summary

Trend to equilibrium solution for the discrete Safronov–Dubovskiĭ aggregation equation with forcing

Contents

Differential and integral equations, dynamical systems and control theory

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28888 results in Differential and integral equations, dynamical systems and control theory

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