7 papers
On the potential lack of response in a model of second-harmonic generation. A computer-assisted proof
Miguel Ayala, Dominic Blanco, Fioralba Cakoni +2
This paper provides a rigorous computer-assisted proof of the existence of generalized transmission eigenvalues arising in nonlinear optics in the context of high-order harmonic ge…
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…
Proving the existence of localized patterns, periodic solutions, and branches of periodic solutions in the 1D Thomas model
Dominic Blanco
In this paper, we present a general framework for constructively proving the existence of stationary localized solutions, spatially periodic solutions, and branches of spatially pe…
Proving periodic solutions and branches in the 2D Swift Hohenberg PDE with hexagonal and triangular symmetry
Dominic Blanco
In this article, we enforce space group symmetries in Fourier series to rigorously prove the existence of smooth, periodic solutions in partial differential equations (PDEs) with h…
Proving the existence of localized patterns and saddle node bifurcations in 1D activator-inhibitor type models
Dominic Blanco, Matthieu Cadiot, Daniel Fassler
In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activator-…
Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
Dominic Blanco, Matthieu Cadiot
In this article, we extend the framework developed in \cite{unbounded_domain_cadiot} to allow for rigorous proofs of existence of smooth, localized solutions in semi-linear partial…
The 2D Gray-Scott system of equations: constructive proofs of existence of localized stationary patterns
Matthieu Cadiot, Dominic Blanco
In this article, we present a comprehensive framework for constructing smooth, localized solutions in systems of semi-linear partial differential equations, with a particular empha…