Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties

TL;DR

This paper establishes the existence of weak solutions for a nonlocal fourth-order parabolic equation modeling MEMS with heterogeneous dielectric properties, leveraging its gradient flow structure.

Contribution

It introduces a variational approach to prove existence results for a complex evolution model in MEMS with heterogeneous materials.

Findings

Existence of weak solutions demonstrated

Utilizes gradient flow structure for analysis

Applicable to MEMS with diverse dielectric properties

Abstract

The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with heterogeneous dielectric properties.