Applied Analysis

Seminar information archive ~03/04Next seminarFuture seminars 03/05~

Date, time & place Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)


16:00-18:10   Room #002 (Graduate School of Math. Sci. Bldg.)
Arnaud Ducrot (University of Bordeaux 2) 16:00-17:00
Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections (ENGLISH)
[ Abstract ]
This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.
Enrique Zuazua (Basque Center for Applied Mathematics) 17:10-18:10
Some open problems in PDE control (ENGLISH)
[ Abstract ]
The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.

From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location
of the controller, nonlinearity in the equation,...)

In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:
1.- Semilinear wave equations and their control properties.
2.- Microlocal optimal design of wave processes
3.- Sharp observability estimates for heat processes.
4.- Robustness on the control of finite-dimensional systems.
5.- Unique continuation for discrete elliptic models
6.- Control of Kolmogorov equations and other hypoelliptic models.