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.
| Original language | English |
|---|---|
| Pages (from-to) | 1175-1200 |
| Number of pages | 26 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 43 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - Mar 2023 |
Keywords
- Bilaplacian eigenvalues
- Cahn-Hilliard equation
- bulk-boundary eigenvalues
- domain perturbation
- dynamic boundary conditions
- eigenfunctions on balls and annulus
- eigenvalue bifurcation