On Convergence of Solutions to Equilibria for Fully Nonlinear Parabolic Systems with Nonlinear Boundary Conditions

摘要

Convergence to stationary solutions in fully nonlinear parabolic systems withgeneral nonlinear boundary conditions is shown in situations where the set ofstationary solutions creates a $C^2$-manifold of finite dimension which isnormally stable. We apply the parabolic H\"older setting which allows to dealwith nonlocal terms including highest order point evaluation. In this directionsome theorems concerning the linearized systems is also extended. As anapplication of our main result we prove that the lens-shaped networks generatedby circular arcs are stable under the surface diffusion flow.