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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
Analysis of a degenerate parabolic system for cell dynamics in intestinal crypts
Ahmad El Hajj, Mohamad El Hajj Chehade, Antoine Zurek
In this work, we study a system of degenerate parabolic equations modeling the dynamics of multiple cell populations in intestinal crypts. The model describes cell division, differ…