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math.AP2026
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…
math.AP2026
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*} -Îu -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equat…