So we finish our session with the talk by Lorenzo Liberani, who is a postdoctoral researcher

here at the chair.

Please.

Okay, thank you.

So today I'm going to discuss about, I will bring the topic back to more like abstract

mathematics and but I, let's see, I was inspired by the talk of yesterday by Professor Chardon

on the Yaponov Functionals, right, on discovering the Yaponov Functionals and I thought, well,

I recently published a paper where we introduced an algorithm to discover the Yaponov Functionals.

So I understand this will not be machine learning but I hope you will find it interesting anyway.

The paper in question is the one you see here.

So as the title says, it is concerned with the asymptotic dynamics of hyperbolic systems

with most symmetric realization.

This was joint work with Timotei Krenbarad, which was here at the chair until last year,

Ling-Yun Shou and obviously Professor Zouzoua.

So this kind of topic here gets very, let's say, technical very quickly.

So I tried to keep it as simple as I could and I also didn't want to bore you with technical

details.

So what I did is that I structured this talk like a video game.

So you will help me solve the levels of this video game and hopefully at the end of the

talk you will understand more or less how our algorithm works.

And of course you will have to indulge me.

I will not be as precise as I should be probably but I just want to give you the main idea

and then of course we can discuss details together later.

So the video game is called Does the energy of the system of hyperbolic partial differential

equations decay?

Which is not a good title but I'm working on it.

However, it has all the ingredients for what we want to do.

So we have a system of hyperbolic partial differential equations.

To this system is associated an energy and we want to know if as time goes to infinity

this energy will go to zero.

So in any video game the first level is always a tutorial.

So let's start with a very simple equation.

This is not even a system.

This is the easiest hyperbolic equation you can think of and let's see what are the rules

of the game.

So the equation we are given is partial derivative in time plus partial derivative in space.

This is the general structure for an hyperbolic equation plus u equal to zero.

So here the space variable and this is very important in this work will always belong

to R, so to the unbounded domain and the energy of this system is always the L2 norm of the

solution.

So whenever you see the symbol of a norm in this talk this is the L2 norm.

It's not specified but it's always the L2 norm.

So the question is always the same.

Does the energy of the system decay as time goes to infinity?

What do you say?

I don't know.

Unfortunately, Enrique is not here.

When I presented this the first time it was the first to raise his hand because obviously

for him it's easy.

Who says yes?