2019/06/28 by Ourania Drosinou, Nikos I. Kavallaris, Drosinou, Ourania +4 · 1 citation
Computer Science · Engineering · Mathematics · #35J60 #74G55 #74K15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems #Primary 35K55 #Secondary 74H35 #Stability and Controllability of Differential Equations #math.AP #msc:35J60 #msc:35K55 #msc:74G55 #msc:74H35 #msc:74K15
paper · pdf · doi:10.48550/arxiv.1906.12093
32 pages, 14 figures, Submitted to journal
openalex publication_date 2019/06/28 · arxiv created 2021/04/10 · arxiv updated 2021/04/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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. Initially we study the steady-state problem in one dimension and we present some numerical results regarding its bifurcation diagram. Next the N-dimensional nonlocal problem steady-state problem is investigated and a Pohozaev-type identity is first obtained which then facilitates derivation of an estimate of the pull-in voltage for radially symmetric domains. Later the time-dependent problem is investigated and global-in-time as well as quenching results are obtained again for general and radially symmetric domains. We close the current work with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented verifying the obtained analytical results.