We are pleased to announce that our 2019 Michalik Lecture will be given by Professor Enrique Zuazua.
Title: Reaction-diffusion models: dynamics, control and numerics
Reaction-diffusion equations are ubiquitous in a variety of fields including combustion and population dynamics.
There is an extensive mathematical literature addressing the analysis of steady state solutions, traveling waves, and their stability, among other properties.
Control problems arise in many applications involving these models. Often times, control and/or state constraints emerge as intrinsic requirements of the processes under consideration. There is also a broad literature on the control of those systems, addressing, in particular, issues such as the possibility of driving the system to a given final configuration in finite time. But, the necessity of preserving the natural constraints of the process are rarely taken into account.
In this lecture we shall present the recent work of our team on the Fisher-KPP and Allen-Canh or bistable model, showing results of two different types depending of the initial and final states under consideration. First, the fact that, in some cases, constrained controllability for large enough time can be achieved, but that there is a minimal waiting time for the property to hold. And, second, negative results showing the existence of threshold effects, so that some targets can never be achieved.
We shall also present some numerical experiments which indicated that optimal trajectories are often quite complex, and hard to deduce form purely analytical arguments.
Dr. Zuazua's fields of specialization cover Partial Differential Equations, Systems Control and Numerical Analysis. These interconnected fields have as ultimate goal the modelling, analysis, computer simulation and control and design of natural phenomena and other problems arising in R+D+i.
Location and Address
University Club Ballroom A