Bulk-Boundary eigenvalues for Bilaplacian problems

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...

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Detalles Bibliográficos
Autores: Buoso, Davide, Falcó, Carles, González, María del Mar, Miranda, Manuel
Tipo de recurso: conjunto de datos
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2022
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/340214
Acceso en línea:http://hdl.handle.net/10261/340214
Access Level:acceso abierto
Palabra clave:Dynamic boundary conditions
Domain perturbation
Bilaplacian eigenvalues
Bulk-boundary eigenvalues
Eigenfunctions on balls and annulus
Eigenvalue bifurcation
Cahn-Hilliard equation
Descripción
Sumario: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.