Premium
A study of a nonlocal problem with Robin boundary conditions arising from technology
Author(s) -
Drosinou Ourania,
Kavallaris Nikos I.,
Nikolopoulos Christos V.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7393
Subject(s) - cantilever , mathematics , work (physics) , boundary value problem , current (fluid) , boundary (topology) , numerical analysis , voltage , mathematical analysis , robin boundary condition , identity (music) , neumann boundary condition , physics , acoustics , quantum mechanics , engineering , thermodynamics , aerospace engineering
In the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro‐electro‐mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady‐state problem is investigated estimates of the pull‐in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull‐in voltage for radially symmetric N ‐dimensional domains. Next a detailed study of the time‐dependent problem is delivered and global‐in‐time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model.