Stationary coexistence of hexagons and rolls via rigorous computations

Authors: Van den berg, Jan Bouwe; Deschènes, Andréa; Lessard, Jean-Philippe; Mireles James, Jason D.
Abstract: In this work we introduce a rigorous computational method for finding heteroclinic solutions of a system of two second order differential equations. These solutions correspond to standing waves between rolls and hexagonal patterns of a two-dimensional pattern formation PDE model. After reformulating the problem as a projected boundary value problem (BVP) with boundaries in the stable/unstable manifolds, we compute the local manifolds using the parameterization method and solve the BVP using Chebyshev series and the radii polynomial approach. Our results settle a conjecture by Doelman et al. [European J. Appl. Math., 14 (2003), pp. 85–110] about the coexistence of hexagons and rolls.
Document Type: Article de recherche
Issue Date: 4 June 2015
Open Access Date: 16 May 2016
Document version: VoR
This document was published in: SIAM Journal on applied Dynamical Systems, Vol. 14 (2), 942–979 (2015)
Society of Industrial and Applied Mathematics
Alternative version: 10.1137/140984506
Collection:Articles publiés dans des revues avec comité de lecture

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