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.

中文翻译：

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具有异质介电特性的MEMS演化模型的变分解决方案

利用其潜在的梯度流结构，显示了非局部半线性四阶抛物方程的障碍问题的弱解的存在。该模型控制具有异构介电特性的微机电系统的动力学。