Bifurcation of the equivariant minimal interfaces in a hydromechanics problem. (English) Zbl 0942.58025

Borisovich, A. Y.; Marzantowicz, W.

Abstr. Appl. Anal. 1, No. 3, 291-304 (1996).

A variational bifurcation problem about the capillary interface of two fluids with densities \(\rho_1\), \(\rho_2\), \(\rho_2-\rho_1 >0\) in a cylinder with a section \(\Omega\subset \mathbb{R}^2\), \(w_{\mid{\partial\Omega}}=0\), is considered. The case of 2-dimensional kernel of the linearized operator is investigated.

Reviewer: Boris V.Loginov (Ul’yanovsk)

MSC:

58E09	Group-invariant bifurcation theory in infinite-dimensional spaces
58E30	Variational principles in infinite-dimensional spaces
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
76A99	Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena

Keywords:

hydromechanics; bifurcation