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On semi‐linear elliptic equation arising from Micro‐Electromechanical Systems with contacting elastic membrane
Author(s) -
Chen Huyuan,
Wang Ying,
Zhou Feng
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700333
Subject(s) - bounded function , domain (mathematical analysis) , dirichlet boundary condition , elliptic curve , boundary value problem , nonlinear system , boundary (topology) , mathematical analysis , membrane , mathematics , dirichlet problem , physics , chemistry , quantum mechanics , biochemistry
This paper is concerned with the nonlinear elliptic problem − Δ u = λ ( a − u ) 2in a bounded domain Ω of R N with Dirichlet boundary conditions. This problem arises from Micro‐Electromechanical Systems devices in the case that the elastic membrane contacts the ground plate on the boundary. We analyze the properties of minimal solutions to this equation when λ > 0 and the function a : Ω ¯ → [ 0 , 1 ]satisfying a ( x ) ≥ κ dist( x , ∂ Ω ) γfor some κ > 0 and γ ∈ ( 0 , 1 ) . Our results show how the boundary decay of the membrane works on the solutions and pull‐in voltage λ.