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Brenier, Yann (Université de NiceSophiaAntipolis)  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, HamiltonJacobi, ideal MHD...) will be discussed.  

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.  

Brenier, Yann (Université de NiceSophiaAntipolis)  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, HamiltonJacobi, ideal MHD...) will be discussed.  

Blanchet, Adrien (Université des Sciences et Technologies de Lille)  Seminarroom C206 + C207  Tue, 11. Sep 07, 15:00 
Entropy methods applied to the KellerSegel system (1/2)  

Brenier, Yann (Université de NiceSophiaAntipolis)  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, HamiltonJacobi, ideal MHD...) will be discussed.  

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.  

Blanchet, Adrien (Université des Sciences et Technologies de Lille)  Seminarroom C206 + C207  Thu, 13. Sep 07, 10:00 
Entropy methods applied to the KellerSegel system (2/2)  

Di Francesco, Marco (Università di L'Aquila)  Seminarroom C206 + C207  Thu, 13. Sep 07, 14:30 
A contraction result in Wasserstein distance for 1d scalar conservation laws.  

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)  

Toscani, Giuseppe (Università 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.  

Toscani, Giuseppe (Università 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.  

Toscani, Giuseppe (Università 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.  

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)  

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)  
 

Carrillo, José Antonio (Universitat Autònoma de Barcelona)  Seminarroom C206 + C207  Fri, 21. Sep 07, 10:00 
Contractions in Wasserstein distances and applications  

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