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math.AP2025
Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
Dominic Blanco, Matthieu Cadiot
In this article, we extend the framework developed in \cite{unbounded_domain_cadiot} to allow for rigorous proofs of existence of smooth, localized solutions in semi-linear partial…
math.AP2025
Stability analysis for localized solutions in PDEs and nonlocal equations on
Matthieu Cadiot
In this paper, we present a general methodology for investigating the linear stability of localized solutions in PDEs and nonlocal equations on . More specifically, w…
math.AP2025
Recent advances about the rigorous integration of parabolic PDEs via fully spectral Fourier-Chebyshev expansions
Matthieu Cadiot, Jean-Philippe Lessard
This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebys…