An elastic body $D$ vibrates. Dirichlet conditions are set on a part of its boundary $\partial D_u$, and Neumann conditions are set on the rest of the boundary $\partial D_p$. Difficulty: $\partial D_u$ and, correspondingly, $\partial D_p$ change with time (in a known way). That is fixed region is "crawling" over the boundary.
I tried to google with many combinations of "Dirichlet", "boundary conditions", "time-dependent", etc, but always got pretty standard things. I guess I'm missing the right keyword.
What is the name of such boundary conditions? Are there any traps in solving such a problem, for example, by FEM? Are there any references?
Thanks!