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math.AP2025
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-…
math.AP2025
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…