Abstract
The model of electrostatic Micro-Electromechanical System (MEMS) is considered without/with an external pressure. The model represents nonlinear elliptic or parabolic problem due to the steady or non-steady state problem, respectively. To obtain exact solutions in an explicit form, the symmetry analysis is considered. With symmetries, the transformations are obtained and by means of these transformations, solvable equations are hold. The obtained results have a major role in the literature so that the considered equation is seen in a large-scale applications.
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