2 citations · 3 across the 4 of their papers we have counts for
6 papers
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…
Numerical Analysis of differential equations on weighted Sobolev spaces: beyond classical orthogonal polynomials
Maxime Breden, Hugo Chu
We lay mathematical foundations for the Numerical Analysis of differential equations on Sobolev spaces weighted by a Gibbs probability measure $ν(\mathrm{d} x) = e^{-V(x)}\mathrm{d…
Rigorous enclosure of Lyapunov exponents of stochastic flows
Maxime Breden, Hugo Chu, Jeroen S. W. Lamb +1
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assis…
Validated enclosure of renormalization fixed points via Chebyshev series and the DFT
Maxime Breden, Jorge Gonzalez, J. D Mireles James
This work develops a computational framework for proving existence, uniqueness, isolation, and stability results for real analytic fixed points of -th order Feigenbaum-Cvitanovi…
Detecting random bifurcations via rigorous enclosures of large deviations rate functions
Alexandra Blessing, Alex Blumenthal, Maxime Breden +1
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time L…
Constructive proofs for some semilinear PDEs on
Maxime Breden, Hugo Chu
We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -Δu -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equati…