Wellposedness of an elliptic-dispersive coupled system for MEMS

In this work, we study the local wellposedness of solution to a nonlinear elliptic-dispersive coupled system which serves as model for Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device consists two parallel plates separated by gas-filled thin gap. The modelling combines linear elliptic equation gas pressure with semilinear dispersive gap width. We show local-in-time existence strict solutions system, combining regularity results equation, Lipschitz continuous dependence its on that and then resulting abstract problem. Semigroup approaches are key solve