10 citations · 16 across the 7 of their papers we have counts for
8 papers
Computer-assisted proofs of periodic solutions of state-dependent delay equations beyond perturbative regimes
Jan Bouwe van den Berg, Maxime Breden, Matthieu Cadiot +2
Rigorous existence results for periodic solutions of state-dependent delay differential equations (SDDEs) are scarce outside perturbative regimes, where the equation is close to an…
Rigorous Validation of Cusp Bifurcations of Stationary Periodic Patterns in Partial Differential Equations
Dominic Blanco, Jean-Philippe Lessard
In this paper, we present a computer-assisted framework for the rigorous validation of cusp bifurcations of spatially symmetric stationary periodic patterns in parabolic semilinear…
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,…
Periodic localized traveling waves in the two-dimensional suspension bridge equation
Lindsey van der Aalst, Jan Bouwe van den Berg, Jean-Philippe Lessard
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional ca…
Cusp bifurcations: numerical detection via two-parameter continuation and computer-assisted proofs of existence
Jean-Philippe Lessard, Alessandro Pugliese
This paper introduces a novel computer-assisted method for detecting and constructively proving the existence of cusp bifurcations in differential equations. The approach begins wi…
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…
A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
Gabriel William Duchesne, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular…