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

2014/03/18 by Helmut Abels, Abels, Helmut, Nasrin Arab +3
Computer Science · Mathematics · #35B35 #35B65 #35K50 #35K55 #37L10 #53C44 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1403.4526

openalex publication_date 2014/03/18 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Convergence to stationary solutions in fully nonlinear parabolic systems with\ngeneral nonlinear boundary conditions is shown in situations where the set of\nstationary solutions creates a C²-manifold of finite dimension which is\nnormally stable. We apply the parabolic H "older setting which allows to deal\nwith nonlocal terms including highest order point evaluation. In this direction\nsome theorems concerning the linearized systems is also extended. As an\napplication of our main result we prove that the lens-shaped networks generated\nby circular arcs are stable under the surface diffusion flow.\n

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