CRM: Centro De Giorgi
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Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation

On the existence of quasipattern solutions of the Swift-Hohenberg equation and of the Rayleigh-Benard convection problem

speaker: Gérard Iooss (IUF, Université de Nice, Laboratoire J.A.Dieudonné)

abstract: This work is made in collaboration with A. M. Rucklidge (Leeds). Quasipatterns (two-dimensional patterns which are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this talk, we consider 8 -fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift--Hohenberg equation. We prove that a formal solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution of the pattern-forming PDE up to an exponentially small error. Considering now the hydrodynamic Rayleigh-Benard convection problem, we are able to prove the same type of result for a steady quasipattern convective regime.

Tue 13 Oct, 9:00 - 10:00, Aula Dini
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