Per a qualsevol qüestió o incidència que tingueu no dubteu en contactar amb els organitzadors: Pau Martín i Jezabel Curbelo (UPC), i/o Arturo Vieiro (UB)

Dia: Dimecres, 15 de maig de 2024

Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.

- Hora: 16h00m

A càrrec de: Fenfen Wang, Universitat de Barcelona

Títol: Response solution to ill-posed Boussinesq equation with quasi-periodic forcing of Liouvillean frequency.

Resum: We focus on the existence of response solution (i.e.,quasi-periodic solution with the same frequency as the forcing) for the quasi-periodically forced generalized ill-posed Boussinesq equation, where the forcing frequency is Liouvillean (beyond Diophantine or Brjuno frequency). The proof is based on a modified Kolmogorov-Arnold-Moser (KAM) iterative scheme. We need to, at every step of KAM iteration, construct a symplectic transformation in a such way that the composition of these transformations reduce the original system to a new system which possesses zero as equilibrium. Note that the model under consideration is ill-posed and has complicated Hamiltonian structure. This makes homological equations appearing in KAM iteration to be different from the ones in the classical infinite-dimensional KAM theory. We strengthen the existing results in the literature where the system is well-posed or the forcing frequency is assumed to be Diophantine.

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Last updated: Mon May 13 13:12:15 2024