Bifurcation for a free boundary problem modeling a protocell

In this paper we consider a free boundary problem for a physico-chemical model of a protocell. This model of a self-maintaining unity or a protocell is based on the reaction and diffusion process, and a mechanism of self-control of the boundary. For any positive radius RR, there exists a radially symmetric solution with radius r=Rr=R. In the more realistic three-space-dimensional case, we give a proof that there exist symmetry-breaking bifurcation branches of solutions with free boundary r=R+ϵYn,0(θ)+O(ϵ2)(n≥2,even) for small |ϵ||ϵ|, where Yn,0Yn,0 is the spherical harmonic of mode (n,0)(n,0).