Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1718-1733.

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Well-Posedness of a Fourth Order Parabolic Equation Modeling MEMS

Baishun Lai(),Qing Luo*()   

  1. School of Mathematics and Statistics, Hunan Normal University, Changsha 410081
  • Received:2020-09-18 Online:2021-12-26 Published:2021-12-02
  • Contact: Qing Luo;
  • Supported by:
    the NSFC(11971148)


In this paper, we consider a fourth order evolution equation involving a singular nonlinear term $\frac{\lambda}{(1-u)^{2}}$ in a bounded domain $\Omega \subset \mathbb{R}^{n}$. This equation arises in the modeling of microelectromechanical systems. We first investigate the well-posedness of a fourth order parabolic equation which has been studied in [1], where the authors, by the semigroup argument, obtained the well-posedness of this equation for $n\leq2$. Instead of semigroup method, we use the Faedo-Galerkin technique to construct a unique solution of the fourth order parabolic equation for $n\leq7$, which completes the result of [1].

Key words: Electrostatic MEMS, Fourth order evolution equation, Well-posedness

CLC Number: 

  • O175