Bianca Morelli Rodolfo Calsavara - UNICAMP

Título:

Local exact controllability for a regulatory genes network.

Resumo:

A regulatory genes network plays an important role in the whole life process, including cellular differentiation, metabolism, cell cycle, signal transduction (i.e., when a cell converts one type of signal or stimulus into another), etc. In this work, it is considered a simplified biological model incorporating the genes FlbA, FlbB, FlbC, FlbD, brlA and PkaA, which act in the cell division of some types of fungi, and three external controls. This model is given by a system of initial and boundary conditions containing coupled nonlinear parabolic partial differential equations. The main result is, under certain conditions, the exact local controllability to a constant suitable trajectory by using less control functions than equations and these functions having arbitrarily small support. The main difficulties of this work are to deal with the nonlinearities of the equations and of the fact that we have less control functions than equations. The idea to deal with this problem is: to use Kalman rank condition (given in [1]) to obtain the exact controllability for a homogeneous linearized system; the ideas of [2] to obtain the exact controllability for a non-homogeneous linearized system; and the Liusternik's Inverse Mapping Theorem to obtain the local exact controllability for the non linear system.

This is a joint work with Enrique Fernández-Cara (U. de Sevilla) and André R. Lopes (PUC-Rio).

References

[1] F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. Gonzalez-Burgos, A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems, Journal of Evolution Equations, volume 9 (2), 2009, pp 267-291.

[2] J. M. Coron, P. Lissy, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components, Inventiones Mathematicae, volume 198, Issue 3, pp 833-880.

Horário:

Ter 19/02 dàs 14:50-15:40