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• W246508170 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." @default.
• W246508170 created "2016-06-24" @default.
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• W246508170 date "2015-01-01" @default.
• W246508170 modified "2023-09-27" @default.
• W246508170 title "Stationary Coexistence of Hexagons and Rolls via Rigorous Computations" @default.
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• W246508170 doi "https://doi.org/10.1137/140984506" @default.
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