2011/09/15 by Parinya Sa Ngiamsunthorn, Ngiamsunthorn, Parinya Sa
Computer Science · Engineering · Mathematics · #35B20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Boundary value problem #Dirichlet boundary condition #Dirichlet distribution #Dynamical Systems (math.DS) #FOS: Mathematics #Invariant (physics) #Invariant manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Perturbation (astronomy) #Physics #Primary 37L05 #Pure mathematics #Secondary 35K58 #Stability and Controllability of Differential Equations #Stable manifold #math.AP #math.DS #msc:35B20 #msc:35K58 #msc:37L05
paper · pdf · doi:10.48550/arxiv.1109.3260
arxiv created 2011/09/15 · openalex publication_date 2011/09/15 · arxiv updated 2011/09/16 · openalex created_date 2025/10/24 · openalex updated_date 2026/08/05
We study the effect of domain perturbation on invariant manifolds for\nsemilinear parabolic equations subject to Dirichlet boundary condition. Under\nMosco convergence assumption on the domains, we prove the upper and lower\nsemicontinuity of both the local unstable invariant manifold and the local\nstable invariant manifold near a hyperbolic equilibrium. The continuity results\nare obtained by keeping track of the construction of invariant manifolds in P.\nW. Bates and C. K. R. T. Jones [Dynam. Report. Ser. Dynam. Systems Appl. Vol.\n2, 1--38, 1989].\n