**May 22, 2015 at 09:30**

**Speaker(s):**
**Laurent GOSSE, Martin LAZAR and Jérôme LOHÉAC**

**Center(s): **Istituto per le Applicazioni del Calcolo-Roma-Italy, University of Dubrovnik-Croatia and Institut de Recherche en Communications et Cybernétique de Nantes-France.

It will be held in BCAM-Basque Center For Applied Mathematics,, located at Alameda Mazarredo, 14-Bilbao , on the

__22nd May 2015__
**Invited Speakers: **
**Laurent GOSSE **

Istituto per le Applicazioni del Calcolo, Roma, Italy
ERROR ESTMATES FOR SOURCE TERM PROBLEMS AND APPLICATIONS

New error estimates for 1D systems of balance laws are presented, relying on Bressan-Liu-Yang L1 stability theory. These error bounds are applied to a simple kinetic model of chemotaxis dynamics, and especially its hydrodynamic limit. Then a nonlinear system of 1+1 relativistic, so called "dilaton" (or R=T), gravity will be presented.

**Martin LAZAR **

University of Dubrovnik, Croatia
AVERAGED CONTROL

In practical applications, the models under consideration are often not completely known, submitted to unknown or uncertain parameters. Thus it is important to develop robust analytical and computational methods allowing to deal with parameter-dependent systems in a stable and computationally efficient way.

As a first step in that direction, the notion of averaged control was introduced recently. Its goal is to control the average of parameter-dependent system components by a single control. The notion is equivalent to the averaged observability, by which the energy of the system is recovered by observing the average of solutions on a suitable subdomain.

The assumptions and results of the theory will be presented on an example of parameter dependent wave equations.

**Jérôme LOHÉAC**

Institut de Recherche en Communications et Cybernétique de Nantes, France
AVERAGAD AND SIMULTANEOUS CONTROL OF A PARAMETER DEPENDENT SYSTEM

In this talk, I will consider the parameter dependent system d/dt y(z,t)=A(z) y(z,t)+B(z) u(t), with y(z,t) the state of the system at time t, u the control and z a parameter.

Since the control u is assumed to be independent of the parameter z, we will see that it is in general difficult to control all the solutions y(z,T).

Let us now assume that the parameter z is a random variable known through its probability density measure P. It is then natural to try to control the system's output expectation: int y(z,t) dP(z).

In a first part, we will recall some averaged controllability results.

And in a second part, I will present a penalty method in order to find (if it exists) a simultaneous control.

For further information, please contact:

**Irantzu Elespe** at

** ielespe@bcamath.org**