Study On The Well-posedness Of Fourth Order Parabolic MEMS Equations With Nonlocal Nonlinear Terms

In this paper,we consider the well posedness of the four order parabolic equation with nonlocal singular nonlinear terms on bounded domains:(?)which describe the dynamics behavior of the Electrostatically actuated microelectromechanical systems(MEMS).Since the maximum principle,Harnack inequality,iteration argument,which are the basic tools to study the corresponding second parabolic operator,are no longer valid for equation(0.1),less attention has been dedicated to(0.1).In this paper,we will use Faedo-Galerkin skill to establish the well-posedness of equation(0.1)in the case n?7.The full text is divided into three chapters.The first chapter mainly introduces the research background of the equation(0.1);In the second chapter,we first introduce some preliminaries,which include some basic properties and inequalities of Lp space and Sobolev space;In the third chapter,we establish the existence and uniqueness of the equation(0.1)by the Galerkin method and the contraction mapping theorem.