Abels, Helmut and Arab, Nasrin and Garcke, Harald (2015) On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions. JOURNAL OF EVOLUTION EQUATIONS, 15 (4). pp. 913-959. ISSN 1424-3199, 1424-3202
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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 Holder 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LINEARIZED STABILITY ANALYSIS; SURFACE-DIFFUSION; STATIONARY SOLUTIONS; TRIPLE JUNCTIONS; HYPERSURFACES; FLOW; Fully nonlinear parabolic systems; General nonlinear boundary conditions; Normally stable; Surface diffusion flow; Triple junctions; Lens-shaped network |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2019 08:06 |
| Last Modified: | 06 May 2019 08:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/4404 |
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