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UID:20251122T001325EST-3722Avj6NW@132.216.98.100
DTSTAMP:20251122T051325Z
DESCRIPTION:Title: Computer-assisted proofs for dynamical systems\n\nAbstra
 ct: \n\nTo understand the global behavior of a nonlinear system\, the firs
 t step is to study its invariant set. Indeed\, specific solutions like ste
 ady states\, periodic orbits and connections between them are building blo
 cks that organize the global dynamics. While there are many deep\, general
  and theoretical mathematical results about the existence of such solution
 s\, it is often difficult to apply them to a specific example. Besides\, w
 hen dealing with a precise application\, it is not only the existence of t
 hese solutions\, but also their qualitative properties that are of interes
 t. In that case\, a powerful and widely used tool is numerical simulations
 \, which is well adapted to the study of an explicit system and can provid
 e insights for problems where the nonlinearities hinder the use of purely 
 analytical techniques. However\, one can do even better. Using numerical r
 esults as a starting point\, and combining them with a posteriori estimate
 s\, one can then get rigorous results and prove the existence of a genuine
  solution close to the numerical one. In this talk\, I will explain how su
 ch computer-assisted theorem can be obtained. I will then focus on some ex
 amples where these techniques can be useful\, namely to study non homogene
 ous steady states of cross-diffusion systems\, and to prove the existence 
 of periodic solutions of the Navier-Stokes equations in a Taylor-Green flo
 w.\n\n \n
DTSTART:20171017T190000Z
DTEND:20171017T200000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Maxime Breden (Technical University of Munich)
URL:/mathstat/channels/event/maxime-breden-technical-u
 niversity-munich-278117
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