Direct and inverse problems related to MEMS

This paper deals with direct and inverse evolution problems which come up in studying micro-electro-mechanical-systems: here we consider a nonlinear and nonlocal MEMS model. The inverse problem consists of recovering a time-varying Coulomb potential by exploiting some accessible measurements, which depend on the dynamic displacement of the system. Local existence, uniqueness and continuous dependence results are proved for both direct and inverse problems.