Papers

Existence proofs of traveling wave solutions on an infinite strip for the suspension bridge equation and proof of orbital stability (with L. van den Aalst, submitted 2025)

Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models (with D. Blanco and D. Fassler, submitted 2025)

Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE (with D. Blanco, submitted 2025)

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, CNSNS 2025)

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)