Papers

Stability analysis for localized solutions in PDEs and nonlocal equations on R^m (submitted 2025)

Recent advances about the rigorous integration of parabolic PDEs via fully spectral Fourier-Chebyshev expansions (with JP. Lessard, submitted 2025)

Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs (with J. Jaquette, JP. Lessard and A. Takayasu, submitted 2024)

The 2D Gray-Scott system of equations: constructive proofs of existence of localized stationary patterns (with D. Blanco, Nonlinearity 2025)

Constructive proofs of existence and stability of solitary waves in the Whitham and capillary-gravity Whitham equations (Nonlinearity 2025)

Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence (with JP. Lessard and JC. Nave, JDE 2025) 

Rigorous computation of solutions of semi-linear PDEs on unbounded domains via spectral methods (with JP. Lessard and JC. Nave, SIAM Journal on Applied Dynamical Systems 2024)