4 papers · 1 filter
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 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…