Vanishing aspect ratio limit for a fourth-order mems model
  So far most studies on mathematical models for microelectromechanical systems (MEMS) are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the aspect ratio equal to zero in a more complex model involving a moving boundary. A rigorous justification of this derivation is provided here when bending is taken into account. 
Philippe Lauren\c{c}ot, Christoph Walker
math.AP