Surface diffusion with triple junctions: A stability criterion for stationary solutions
نویسندگان
چکیده
We study a fourth order geometric evolution problem on a network of curves in a bounded domain Ω. The flow decreases a weighted total length of the curves and preserves the enclosed volumes. Stationary solutions of the flow are critical points of a partition problem in Ω. In this paper we study the linearized stability of stationary solutions using the H-gradient flow structure of the problem. Important issues are the development of an appropriate PDE formulation of the geometric problem and Poincaré type estimate on a network of curves.
منابع مشابه
Stability analysis of phase boundary motion by surface diffusion with triple junction
The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the H-gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding di...
متن کاملNonlinear stability of stationary solutions for curvature flow with triple junction
In this paper we analyze the motion of a network of three planar curves with a speed proportional to the curvature of the arcs, having perpendicular intersections with the outer boundary and a common intersection at a triple junction. As a main result we show that a linear stability criterion due to Ikota and Yanagida [13] is also sufficient for nonlinear stability. We also prove local and glob...
متن کاملOn the onset of triple-diffusive convection in a layer of nanofluid
On the onset of triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is studied both analytically and numerically. The effects of thermophoresis and Brownian diffusion parameters are also introduced through Buongiorno model in the governing equations. By using linear stability analysis based on perturbation theory and applying normal m...
متن کاملNonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions
The volume preserving fourth order surface diffusion flow has constant mean curvature hypersurfaces as stationary solutions. We show nonlinear stability of certain stationary curves in the plane which meet an exterior boundary with a prescribed contact angle. Methods include semigroup theory, energy arguments, geometric analysis and variational calculus.
متن کاملStability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous cells, whose proliferation is controled by growth factors diffusing in the extracellular medium and binding to the cell surface. We extend the results on the e...
متن کامل