Steady State Bifurcations for Phase Field Crystal Equations with underlying two Dimensional Kernel

This paper is concerned with the study of some properties of stationary solutions to Phase Field Crystal Equations bifurcating from a trivial solution. It is assumed that at this trivial solution, the kernel of the underlying linearized operator has dimension two. By means of the multiparameter method, we give a second order approximation of these bifurcating solutions and analyse their stability properties. The main result states that the stability of these solutions can be described by the variation of a certain angle in a two dimensional parameter space. The behaviour of the parameter curve is also investigated.

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Source https://hal.science/hal-00911041
Author Rougirel, Arnaud, Abourou Ella, Appolinaire
Maintainer CCSD
Last Updated May 8, 2026, 01:16 (UTC)
Created May 8, 2026, 01:16 (UTC)
Identifier hal-00911041
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de mathématiques et applications [UMR 7348] (LMA [Poitiers]) ; Université de Poitiers = University of Poitiers (UP)-Centre National de la Recherche Scientifique (CNRS)
creator Rougirel, Arnaud
date 2013-11-28T00:00:00
harvest_object_id 95a13cea-ac70-47ed-9041-53669811c0ff
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-03-07T00:00:00
set_spec type:UNDEFINED