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Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's"

Location: Seminarroom C206 + C207 Mon, 10. Sep (Opening: 9:00) - Fri, 21. Sep 07
Organisation(s)
WPI
Organiser(s)
José A. Carrillo (UAB Barcelona)
Marco Di Francesco (Univ. L'Aquila)
Speakers: Adrien Blanchet (Université de Lille 1); Yann Brenier (Nice); José A. Carrillo (UAB Barcelona); Marco Di Francesco (University of L'Aquila); Alessio Figalli (SNS Pisa - ENS Lyon); Giuseppe Toscani (Pavia); Juan Luis Vazquez (UAM MAdrid).

Talks in the framework of this event


Brenier, Yann (Université de Nice-Sophia-Antipolis) Seminarroom C206 + C207 Mon, 10. Sep 07, 10:00
Optimal transportation for conservative evolution equations (1/3)
The relevence of optimal transportation techniques for dissipative evolution equations is now very well known (following the seminal paper of Jordan, Kinderlehrer and Otto on the heat equation viewed as a gradient flow on probability measures for the Boltzmann entropy). In this minicourse, applications to conservative evolution equations (such as the Euler equations, multidimensional scalar conservation laws, Hamilton-Jacobi, ideal MHD...) will be discussed.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Figalli, Alessio (Scuola Normale di Pisa - École Normale Supérieure de Lyon) Seminarroom C206 + C207 Mon, 10. Sep 07, 15:00
Incompressible models for the incompressible Euler's equations (1/2)
Following Arnold's interpretation, Euler's equations can be seen as the geodesic equation in the space of measure preserving diffeomorphism. Thus, one can try to find solutions to Euler's equation minimizing the Energy functional with fixed endpoints (this is the usual way to find geodesics on a manifold). It turns out that the study of (a relaxed version of) this problem presents many links with optimal transportation. In this minicourse I will explain the problem in details, I will review the results of Brenier and Shnirelman, and I will present recent results obtained in collaboration with L.Ambrosio.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Brenier, Yann (Université de Nice-Sophia-Antipolis) Seminarroom C206 + C207 Tue, 11. Sep 07, 10:00
Optimal transportation for conservative evolution equations (2/3)
The relevence of optimal transportation techniques for dissipative evolution equations is now very well known (following the seminal paper of Jordan, Kinderlehrer and Otto on the heat equation viewed as a gradient flow on probability measures for the Boltzmann entropy). In this minicourse, applications to conservative evolution equations (such as the Euler equations, multidimensional scalar conservation laws, Hamilton-Jacobi, ideal MHD...) will be discussed.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Blanchet, Adrien (Université des Sciences et Technologies de Lille) Seminarroom C206 + C207 Tue, 11. Sep 07, 15:00
Entropy methods applied to the Keller-Segel system (1/2)
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Brenier, Yann (Université de Nice-Sophia-Antipolis) Seminarroom C206 + C207 Wed, 12. Sep 07, 10:00
Optimal transportation for conservative evolution equations (3/3)
The relevence of optimal transportation techniques for dissipative evolution equations is now very well known (following the seminal paper of Jordan, Kinderlehrer and Otto on the heat equation viewed as a gradient flow on probability measures for the Boltzmann entropy). In this minicourse, applications to conservative evolution equations (such as the Euler equations, multidimensional scalar conservation laws, Hamilton-Jacobi, ideal MHD...) will be discussed.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Figalli, Alessio (Scuola Normale di Pisa - École Normale Supérieure de Lyon) Seminarroom C206 + C207 Wed, 12. Sep 07, 15:00
Incompressible models for the incompressible Euler's equations (2/2)
Following Arnold's interpretation, Euler's equations can be seen as the geodesic equation in the space of measure preserving diffeomorphism. Thus, one can try to find solutions to Euler's equation minimizing the Energy functional with fixed endpoints (this is the usual way to find geodesics on a manifold). It turns out that the study of (a relaxed version of) this problem presents many links with optimal transportation. In this minicourse I will explain the problem in details, I will review the results of Brenier and Shnirelman, and I will present recent results obtained in collaboration with L.Ambrosio.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Blanchet, Adrien (Université des Sciences et Technologies de Lille) Seminarroom C206 + C207 Thu, 13. Sep 07, 10:00
Entropy methods applied to the Keller-Segel system (2/2)
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Di Francesco, Marco (Universitŕ di L'Aquila) Seminarroom C206 + C207 Thu, 13. Sep 07, 14:30
A contraction result in Wasserstein distance for 1-d scalar conservation laws.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Vázquez, Juan Luis (Universidad Autónoma de Madrid) Seminarroom C206 + C207 Mon, 17. Sep 07, 10:00
Recent progress in fast diffusion and geometrical diffusion (1/3)
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Toscani, Giuseppe (Universitŕ di Pavia) Seminarroom C206 + C207 Tue, 18. Sep 07, 10:00
Kinetic models of Maxwell type with applications (1/3)
In these lectures we will introduce and discuss various kinetic models of Boltzmann type, which have a collision kernel independent of the relative velocity (Maxwell type models). These kinetic equations possess an interesting mathematical structure, which in most cases allow to recover a precise rate for the relaxation to equilibrium in terms of different metrics. Applications both to economy and social sciences of these models are presented into details.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Toscani, Giuseppe (Universitŕ di Pavia) Seminarroom C206 + C207 Tue, 18. Sep 07, 15:00
Kinetic models of Maxwell type with applications (2/3)
In these lectures we will introduce and discuss various kinetic models of Boltzmann type, which have a collision kernel independent of the relative velocity (Maxwell type models). These kinetic equations possess an interesting mathematical structure, which in most cases allow to recover a precise rate for the relaxation to equilibrium in terms of different metrics. Applications both to economy and social sciences of these models are presented into details.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Toscani, Giuseppe (Universitŕ di Pavia) Seminarroom C206 + C207 Wed, 19. Sep 07, 10:00
Kinetic models of Maxwell type with applications (3/3)
In these lectures we will introduce and discuss various kinetic models of Boltzmann type, which have a collision kernel independent of the relative velocity (Maxwell type models). These kinetic equations possess an interesting mathematical structure, which in most cases allow to recover a precise rate for the relaxation to equilibrium in terms of different metrics. Applications both to economy and social sciences of these models are presented into details.
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Vázquez, Juan Luis (Universidad Autónoma de Madrid) Seminarroom C206 + C207 Wed, 19. Sep 07, 15:00
Recent progress in fast diffusion and geometrical diffusion (2/3)
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Vázquez, Juan Luis (Universidad Autónoma de Madrid) Seminarroom C206 + C207 Thu, 20. Sep 07, 10:00
Recent progress in fast diffusion and geometrical diffusion (3/3)
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

Carrillo, José Antonio (Universitat Autňnoma de Barcelona) Seminarroom C206 + C207 Fri, 21. Sep 07, 10:00
Contractions in Wasserstein distances and applications
  • Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
  • Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)

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