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PDE Seminar, 2011
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Next seminar:
Nov 8+15+22. Erlend B. Storrøsten, CMA
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Introduction to optimal transport
Abstract: The lectures will be based on the introduction, chapters 1 and 2 of the book "Topics in Optimal Transportation" by Cedric Villani
see also:
http://arxiv.org/abs/1011.2911
Previous / scheduled seminars:
Nov 8+15+22. Erlend B. Storrøsten, CMA
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Introduction to optimal transport
Abstract: The lectures will be based on the introduction, chapters 1 and 2 of the book "Topics in Optimal Transportation" by Cedric Villani
see also:
http://arxiv.org/abs/1011.2911
May 13. Raimund Burger, University of Concepsión, Chile
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Difference schemes stabilized by discrete mollification for
degenerate parabolic equations in two space dimensions
Abstract: The discrete mollification method is a convolution-based filtering procedure for the regularization of ill-posed problems. This method is applied here to stabilize explicit schemes, which were first analyzed by Karlsen & Risebro (2001) for the solution of initial value problems of strongly degenerate parabolic PDEs in two space dimensions. Two new schemes are proposed, which are based on direction-wise and two-dimensional discrete
mollification of the second partial derivatives forming the Laplacian of the diffusion function, respectively. The mollified schemes permit to use substantially larger time steps than the original (basic) scheme. It is proven that both schemes converge to the unique entropy solution of the initial value problem. Numerical examples demonstrate that the mollified schemes are competitive in efficiency, and in many cases significantly more efficient, than the basic scheme.
This presentation is based on joint work with Carlos Daniel Acosta (Universidad Nacional de Colombia, Sede Manizales).
May 6. Frederike Kissling, University of Stuttgart, Germany
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Heterogeneous multiscale methods in porous media flow.
Abstract:
Apr 1. Simone Calogero, University of Granada, Spain
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Hypocoercivity of kinetic Fokker-Planck equations on Riemannian manifolds.
Abstract: A class of linear kinetic Fokker-Planck equations with a non-trivial diffusion matrix and with periodic boundary conditions in the spatial variable is considered. After formulating the problem in a geometric setting, the question of the rate of convergence to equilibrium is studied within the formalism of differential calculus on Riemannian manifolds. Under explicit geometric assumptions on the velocity field, the energy function and the diffusion matrix, it is shown that global regular solutions converge in time to equilibrium with exponential rate. The result is proved by estimating the time derivative of a modified entropy functional, as recently proposed by Villani. For spatially homogeneous solutions the assumptions of the main theorem reduce to the curvature bound condition for the validity of logarithmic Sobolev inequalities discovered by Bakry and Emery. The result applies to the relativistic Fokker-Planck equation in the low temperature regime, for which exponential trend to equilibrium was previously unknown.
Mar 25. Giuseppe Coclite, University of Bari, Italy
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Schrodinger-Maxwell System with Dirac Mass
Abstract: In this lecture we consider a quantistic non-relativistic charged particle (say an electron) that is moving in an hole of potential under the action of an external short range force field. The equations describing this phenomenon are the coupled Schrodinger-Maxwell ones. Moreover, the external short range potential causes the presence of a Dirac mass. We prove the existence of a nontrivial standing wave solution in the electrostatic case. These results were obtained in collaboration with Prof. Helge Holden.
Mar 18. Andrew McMurry, CMA
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Magnetohydrodynamics: Numerical Solution and Astrophysical Applications.
Mar 11. Hermano Frid, IMPA, Brazil
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Homogenization of degenerate porous medium type equations in ergodic algebras
Abstract: http://tinyurl.com/6jy5bz8
Mar 4. Hermano Frid, IMPA, Brazil
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Homogenization of degenerate porous medium type equations in ergodic algebras
Abstract: http://tinyurl.com/6jy5bz8
Feb. 25. Xavier Raynaud, CMA
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Transport equations in biology
Abstract: I will continue to present Chapter 2 from Perthame's book Transport equations in biology.
I will talk about constrained Hamilon-Jacobi
equations which arise in the field of adaptative ecology.
Feb. 10. Xavier Raynaud, CMA
Time/place:
11.15-12.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Transport equations in biology
Abstract: I will finish chapter 1:
* Models of epidemiology (SI,SIR,SEIR)
* Ecological model of competition for resources
* Phytoplankton - Light structure
and start with chapter 2: Adaptative dynamics, an asymptotic point of view
* Structured population and selection principles
* Mutations
In the case where the mutations are small, the modelling equations asymptotically converge to a constrained Hamilton-Jacobi Equation.
Jan 11. Trygve K. Karper, MI / Mechanics division
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Operator splitting for well-posed
Active Scalar equations
Abstract: See attachment.
Organizers:
Nils Henrik Risebro, CMA
Snorre Christiansen, CMA
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