10 citations · 10 across the 11 of their papers we have counts for
13 papers
Finite-time blow-up for the real-valued defocusing energy-supercritical NLW
Matthieu Cadiot, Alexandru D. Ionescu, Stan Palasek
We consider the defocusing nonlinear wave equations , with odd, for real-valued functions on , in the energy-supercritical case. For $(…
Global Bifurcation and the Constructive Existence of Overhanging Periodic Steady Water Waves
Matthieu Cadiot, Susanna Haziot
We provide a constructive existence proof for overhanging periodic gravity water waves with constant vorticity. By introducing a conformal mapping formulation, we parameterize the…
Constructive existence proofs and stability of stationary solutions to parabolic PDEs using Gegenbauer polynomials
Maxime Breden, Matthieu Cadiot, Antoine Zurek
In this paper, we present a computer-assisted framework for constructive proofs of existence for stationary solutions to one-dimensional parabolic PDEs and the rigorous determinati…
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…
Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard +1
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First,…
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…
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…
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…
Rigorous computation of solutions of semi-linear PDEs on unbounded domains via spectral methods
Matthieu Cadiot, Jean-Philippe Lessard, Jean-Christophe Nave
In this article we present a general method to rigorously prove existence of strong solutions to a large class of autonomous semi-linear PDEs in a Hilbert space $H^{l}\subset H^{s}…