Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2.

Abstract

Abstract. We will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this equation has a radially symmetric solution. Our goal is to study the bifurcation which breaks symmetry. In order to establish critical values of bifurcation parameter and buckling modes we will investigate an appropriate linear problem. Our main result on the existence of symmetrybreaking bifurcation will be proved by the use of a variational version of the Crandall-Rabinowitz theorem.Mathematics Subject Classification (2010). 35R35, 34K18.

Subcritical bifurcation of free elastic shell of biological cluster

“…To this end we will use Fact 2.2. From what has already been proved in [1] we havê E ϱϱτ (0, τ k , ω, ν)e k e k = − 2ν+1  π ν+1 k 2 νω < 0.…”

“…In [1], applying the Crandall-Rabinowitz theorem on simple bifurcation points (see [19]) we proved the following.…”