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math.AP2024
The 2D Gray-Scott system of equations: constructive proofs of existence of localized stationary patterns
Matthieu Cadiot, Dominic Blanco
In this article, we present a comprehensive framework for constructing smooth, localized solutions in systems of semi-linear partial differential equations, with a particular empha…
math.AP2024
Constructive proofs of existence and stability of solitary waves in the Whitham and capillary-gravity Whitham equations
Matthieu Cadiot
In this manuscript, we present a method to prove constructively the existence and spectral stability of solitary waves in both the Whitham and the capillary-gravity Whitham equatio…
math.AP2024★ 10 cited
Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence
Matthieu Cadiot, Jean-Philippe Lessard, Jean-Christophe Nave
In this paper, we present a methodology for establishing constructive proofs of existence of smooth, stationary, non-radial localized patterns in the planar Swift-Hohenberg equatio…