4 papers
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…
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…
A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
Gabriel William Duchesne, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular…
Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard +1
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First,…