A study of a nonlocal problem with Robin boundary conditions arising from technology
Kavallaris, Nikos I.; orcid: 0000-0002-9743-8636; email: firstname.lastname@example.org
Nikolopoulos, Christos V.
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AbstractIn 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.
CitationMathematical Methods in the Applied Sciences
DescriptionFrom Wiley via Jisc Publications Router
History: received 2020-08-03, rev-recd 2021-02-18, accepted 2021-02-22, pub-electronic 2021-05-04
Article version: VoR
Publication status: Published