TY - JOUR

T1 - A free boundary problem modeling electrostatic MEMS

T2 - I. Linear bending effects

AU - Laurençot, Philippe

AU - Walker, Christoph

N1 - Funding information: The work of Ph.L. was partially supported by the CIMI (Centre International de Mathématiques et d’Informatique) Excellence program and by the Deutscher Akademischer Austausch Dienst (DAAD) while enjoying the hospitality of the Institut für Angewandte Mathematik, Leibniz Universität Hannover. Partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.

PY - 2014/9/7

Y1 - 2014/9/7

N2 - 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 (formula presented) and (formula presented) 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 (formula presented). Non-existence of steady states is also established when (formula presented) is small enough and (formula presented) is large enough (depending on (formula presented).

AB - 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 (formula presented) and (formula presented) 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 (formula presented). Non-existence of steady states is also established when (formula presented) is small enough and (formula presented) is large enough (depending on (formula presented).

KW - 35B60

KW - 35K91

KW - 35M33

KW - 35Q74

KW - 35R35

UR - http://www.scopus.com/inward/record.url?scp=84919875774&partnerID=8YFLogxK

U2 - 10.1007/s00208-014-1032-8

DO - 10.1007/s00208-014-1032-8

M3 - Article

AN - SCOPUS:84919875774

VL - 360

SP - 307

EP - 349

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -