Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions
Harald Garcke, Kazuo Itô, Yoshihito Kohsaka · SIAM Journal on Mathematical Analysis · 2005
The linearizedstability of stationary solutions to the surface diffusion flow with angle conditions and no-flux conditions as boundary conditions is studied. We perform a linearized stability analysis in which the H -1 -gradient flow structure plays a key role. As a byproduct our analysis also gives a criterion for the stability of critical points of the length functional of curves which come into contact with the outer boundary. Finally, we study the linearized stability of several examples.