Bulk-boundary eigenvalues for Bilaplacian problems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2021 United Kingdom, Spain, Italy Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems, volume 43, pages 1,175-1,200 (issn: 1078-0947, eissn: 1553-5231,

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Authors: Buoso, D; Falcó, C; González, MDM; Miranda, M;

doi: 10.3934/dcds.2022096 , 10.48550/arxiv.2112.05942

arXiv: 2112.05942

handle: 10261/340212 , 11579/150260

Bulk-boundary eigenvalues for Bilaplacian problems

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Abstract

We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary conditions for the Cahn-Hilliard equation. First we consider continuity properties under parameter variation (in which the parameter also affects the domain of definition of the operator). Then we look at the ball and the annulus geometries (together with the punctured ball), obtaining the eigenvalues as solutions of a precise equation involving special functions. An interesting outcome of our analysis in the annulus case is the presence of a bifurcation from the zero eigenvalue depending on the size of the annulus.

25 pages, 5 figures

Countries

United Kingdom, Spain, Italy

Related Organizations

Spanish National Research Council
Spain
University of Oxford
United Kingdom
Autonomous University of Madrid
Spain
Institute for Cross-Disciplinary Physics and Complex Systems
Spain
University of Eastern Piedmont Amadeo Avogadro
Italy

Keywords

35A09, 35B30, 35G05, 35P15, Dynamic boundary conditions, bilaplacian eigenvalues, Estimates of eigenvalues in context of PDEs, Dynamical Systems (math.DS), dynamic boundary conditions, 510, domain perturbation, Cahn-Hilliard equation, Mathematics - Spectral Theory, eigenfunctions on balls and annulu, Mathematics - Analysis of PDEs, eigenfunctions on balls and annulus, bulk-boundary eigenvalue, FOS: Mathematics, Bulk-boundary eigenvalues, Mathematics - Dynamical Systems, Spectral Theory (math.SP), eigenvalue bifurcation, Classical solutions to PDEs, dynamic boundary condition, Eigenfunctions on balls and annulus, Bilaplacian eigenvalue, Boundary value problems for higher-order elliptic equations, bulk-boundary eigenvalues, Domain perturbation, Bilaplacian eigenvalues, Eigenvalue bifurcation, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Analysis of PDEs (math.AP)

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