| Abstract: |
| We analyze the asymptotic behavior of eigenvalues and eigenfunctions for a biharmonic Steklov problem on a thin domain in $\mathbb{R}^n$ collapsing to a segment. In dimension $n=2$, the model describes vibrations of a thin elastic plate with mass concentrated on part of the boundary.
The problem depends on a parameter $\sigma$, representing the Poisson ratio, which plays a key role in the limiting process. As the thickness vanishes, we derive the limit problem and show that the resulting operator exhibits a nontrivial distortion depending on both $\sigma$ and the space dimension $n$.
Based on a joint work with Bauyrzhan Derbissaly. |
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