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math.AP2026
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 $(…
math.AP2026
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…
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…