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Journal of Evolution Equations

, Volume 15, Issue 4, pp 913–959 | Cite as

On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions

  • Helmut AbelsEmail author
  • Nasrin Arab
  • Harald Garcke
Article

Abstract

Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a C 2-manifold of finite dimension which is normally stable. We apply the parabolic Hölder setting which allows to deal with nonlocal terms including highest order point evaluation. In this direction, some theorems concerning the linearized systems are also extended. As an application of our main result, we prove that the lens-shaped networks generated by circular arcs are stable under the surface diffusion flow.

Keywords

Fully nonlinear parabolic systems General nonlinear boundary conditions Normally stable Surface diffusion flow Triple junctions Lens-shaped network 

Mathematics Subject Classification

35B35 35K55 35K50 37L10 53C44 35B65 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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