3 days on Evolution PDEs 2021

On fall September 08th. to September 10th., our Head Enrique Zuazua will give a course on “Dissipativity, hypocoercivity, decay, memory and control” at the “3 days on Evolution PDEs 2021” at Italy, Aula Magna of Collegio Raffaello (Urbino).

WHEN?

Our Head will talk on September 08th, 2021 at 11:20 and September 09, 2021 at 09:10

ATTENDING THIS EVENT

Registration is required, sending an email to evolutionpdes@gmail.com

Abstract.
Often, even when evolution PDEs are of dissipative nature, disclosing its sharp decay properties
is a complex issue. The problem becomes even more intricate when dealing with numerical approximation schemes aiming to guarantee that the numerical solutions are well-behaved asymptotically, in the sense that they preserve the large time properties of the PDE solutions.
In this series of lectures, we will first discuss two paradigmatic examples: partially dissipative
systems and Kolmogorov equations, in which we worked in collaboration with K. Beauchard and
A. Porretta, respectively.
Both models present some analogies, related with the need of disclosing the actual impact of partial diffusion on the decay of solutions and its numerical approximations on systems that are,
apparently, of a hyperbolic nature.
We shall show how to combine Fourier analysis, control theoretical tools and hypocoercivity techniques to address these issues.
We shall also discuss control problems for viscoelastic models, involving memory terms, that induce hidden hyperbolic phenomena.
Following joint work with F. Chaves, Q. Lü, L. Rosier and X. Zhang, we shall show that the model
can be written as a coupled parabolic-ODE system. This will allow us to show the relevance of
employing moving actuation mechanisms to efficiently control the dynamics of the system.
We shall conclude describing a number of open problems and directions of future research.

Purpose of this Conference

The purpose of this conference is to highlight recent developments in the analysis of time-dependent equations, and more generally of evolution problems. The aim is to bring together leading experts working in different fields, whose research interests intersect the scientific topics of the workshop, and to stimulate new interactions and collaborations.
The conference will take place in the beautiful renaissance town of Urbino and will consist in 2 mini-courses and several seminars by invited speakers. We plan to discuss various topics concerning partial differential equations, semigroup theory, geometric analysis and control theory.

SCHEDULE

• Wed. September 8
  9:00 – 9:15. Opening
  11:00 –coffee break
• 11:00. E. Zuazua “Dissipativity, hypocoercivity, decay, memory and control” (Part 1)
  11:30 – 13.15. D. Pallara “An introduction to infinite-dimensional analysis” (Part 1)
  Lunch
  14:30 – 18:00. Seminars
• Thu. September 9
  9:15 –E. Zuazua “Dissipativity, hypocoercivity, decay, memory and control” (Part 2)
• 11:00. D. Pallara “An introduction to infinite-dimensional analysis” (Part 2)
  11:00 – 11: 30. Coffee break

  Lunch
  14:30 – 18:00. Seminars

• Fri. September 10
  9:15 – 13:15. Seminars and closing session

More details at the Official Event page