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math.AP2026
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…
math.AP2025
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…
math.AP2024
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…