A free boundary problem modeling electrostatic MEMS: I. Linear bending effects

作者：Laurencot Philippe; Walker Christoph^*

来源：Mathematische Annalen, 2014, 360(1-2): 307-349.

DOI：10.1007/s00208-014-1032-8

The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem in a non-smooth domain, are investigated. The equation arises in the modeling of microelectromechanical systems and includes two positive parameters and related to the applied voltage and the aspect ratio of the device, respectively. Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as a criterion for global existence excluding the occurrence of finite time singularities which are not physically relevant. Existence of a stable steady state is shown for sufficiently small . Non-existence of steady states is also established when is small enough and is large enough (depending on ).

• 出版日期2014-10