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PDE Seminar, 2012
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Next seminar:
May 15. Randall J. LeVeque, University of Washington, USA
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Finite Volume Methods for Wave Propagation in
Elastic and Poroelastic Materials
Abstract:The Clawpack software (Conservation LAW PACKage, www.clawpack.org)
implements high-resolution finite volume methods for linear and
nonlinear wave propagation problems. The algorithms are based on
the solution of Riemann problems at the interfaces between grid cells. This is a natural approach to solving problems in heterogeneous
media with material discontinuities, and can accurately capture
reflected and transmitted waves. In this talk two applications
will be discussed: 1) Nonlinear elastic waves in periodic structures,
where dispersion introduced by reflections at material interfaces
leads to the appearance of solitary waves. 2) Poroelastic models
for wave propagation in a solid matrix permeated with a fluid, with
application to the study of wave propagation in bone and extracorporeal
shock wave therapy (ESWT).
Previous / scheduled seminars:
May 22. Laura Valentina Spinolo (CNR, Pavia, Italy)
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Viscous approximation of systems of conservation laws in one space
dimension: the initial-boundary value problem.
Abstract: In the first part of the seminar I will overview some results
concerning one-dimensional systems of conservation laws and viscous
approximations of initial-boundary value problems.
The main challenges posed by the
initial-boundary value problem are the possible presence of boundary layer
phenomena and the fact that, in general, the limits of two different viscous
approximation donot coincide.
In the second part of the seminar I will focus on the so-called Riemann
problem and I will discuss results concerning the limits of different
classes of viscous approximations. In particular, I will describe a
possible way of
characterizing the limit. Also, I will establish a uniqueness result
providing conditions sufficient to conclude that the limits of two
different viscous
approximation are the same.
The talk will be based on joint works with S. Bianchini, C. Christoforou
and S. Mishra.
May 15. Randall J. LeVeque, University of Washington, USA
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: Finite Volume Methods for Wave Propagation in
Elastic and Poroelastic Materials
Abstract:The Clawpack software (Conservation LAW PACKage, www.clawpack.org)
implements high-resolution finite volume methods for linear and
nonlinear wave propagation problems. The algorithms are based on
the solution of Riemann problems at the interfaces between grid cells. This is a natural approach to solving problems in heterogeneous
media with material discontinuities, and can accurately capture
reflected and transmitted waves. In this talk two applications
will be discussed: 1) Nonlinear elastic waves in periodic structures,
where dispersion introduced by reflections at material interfaces
leads to the appearance of solitary waves. 2) Poroelastic models
for wave propagation in a solid matrix permeated with a fluid, with
application to the study of wave propagation in bone and extracorporeal
shock wave therapy (ESWT).
Mar 20. Giuseppe M. Coclite, University of Bari, Italy
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: An optimal harvesting problem with measure valued solutions
Abstract:In this lecture we consider a model for the harvesting of marine
resources, described by an elliptic equation. Since the cost
functionals have sublinear growth with respect to the pointwise
intensity of fishing effort, optimal solutions are in general measure-
valued. For the control problem, we prove the existence of optimal strategies. The results were obtained in collaboration with Professors Alberto Bressan and Wen Shen.
Jan 17. Trygve K. Karper, University of Maryland, USA
Time/place:
10.15-11.00 / seminar room B1036 (10th floor) in the Niels Henrik Abel building.
Title: On some biological models of self-organization
Abstract: In nature, groups of individuals organize globally using only local information. For instance, in a school of fish, there are no external forces to coordinate the group, no leader to guide them. Several mathematical models have been proposed to describe self-organization. In this talk, we will consider two of the most famous models; the Keller-Segel model for bacterial chemotaxis and the Cucker-Smale model for flocking. The emphasis will be on recent mathematical results and remaining open questions. Starting from the microscopic description on particle level, we will discuss the derivation of mesoscopic and macroscopic models at the continuum level. Since the motivation for deriving continuum models is largely numerical, we will also discuss distinct numerical challenges with the resulting models.
Organizers:
Kenneth H. Karlsen, CMA
Nils Henrik Risebro, CMA
Snorre Christiansen, CMA
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