10 citations · 10 across the 11 of their papers we have counts for
5 papers · 2 filters
Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models
Dominic Blanco, Matthieu Cadiot, Daniel Fassler
In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activator-…
Existence proofs of traveling wave solutions on an infinite strip for the suspension bridge equation and proof of orbital stability
Lindsey van der Aalst, Matthieu Cadiot
In this paper, we present a computer-assisted approach for constructively proving the existence of traveling wave solutions of the suspension bridge equation on the infinite strip…
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…
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…
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…