Skip to Main content Skip to Navigation
Journal articles

Existence of quasipatterns solutions of the Swift-Hohenberg equation

Abstract : We consider the steady Swift-Hohenberg partial differential equation. It is a one-parameter family of PDE on the plane, modeling for example Rayleigh-Bénard con-vection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane and which are invariant under rotations of angle π/q, q ≥ 4. We solve an unusual small divisor problem, and prove the existence of solutions for small parameter values. Notice a gap in the proof between Lemma 14 and Lemma 15. A forthcomming paper solves the problem.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download
Contributor : Gerard Iooss Connect in order to contact the contributor
Submitted on : Sunday, January 31, 2016 - 10:54:59 AM
Last modification on : Saturday, June 25, 2022 - 11:18:35 PM
Long-term archiving on: : Friday, November 11, 2016 - 10:19:56 PM


Files produced by the author(s)



Boele Braaksma, Gérard Iooss, Laurent Stolovitch. Existence of quasipatterns solutions of the Swift-Hohenberg equation. Archive for Rational Mechanics and Analysis, Springer Verlag, 2014, 211 (3), ⟨10.1007/s00205-013-0627-7⟩. ⟨hal-01265181⟩



Record views


Files downloads