Global bifurcation curves of a regularized MEMS model. (January 2021)
- Record Type:
- Journal Article
- Title:
- Global bifurcation curves of a regularized MEMS model. (January 2021)
- Main Title:
- Global bifurcation curves of a regularized MEMS model
- Authors:
- Lao, Xiaoqing
Pan, Hongjing
Xing, Ruixiang - Abstract:
- Abstract: The two-parameter differential equation u ′ ′ ( x ) + λ ( 1 − u ) 2 − λ ε 2 ( 1 − u ) 4 = 0 with the boundary condition u ( − 1 ) = u ( 1 ) = 0 governs the steady-state solutions from a regularized MEMS model. We prove that there exist two constants ε ˆ ( ≈ 0 . 25458 ) and ε ˇ ( ≈ 0 . 29212 ) such that the bifurcation curve is S-shaped for 0 < ε ⩽ ε ˆ and is strictly increasing for ε ⩾ ε ˇ in the λ, ‖ u ‖ ∞ -plane. This partly confirms the numerical simulations in Lindsay et al. (2014), and also improves a recent result in Iuorio et al. (2019), where the S-shaped curve is proved for sufficiently small ε .
- Is Part Of:
- Applied mathematics letters. Volume 111(2020)
- Journal:
- Applied mathematics letters
- Issue:
- Volume 111(2020)
- Issue Display:
- Volume 111, Issue 2020 (2020)
- Year:
- 2020
- Volume:
- 111
- Issue:
- 2020
- Issue Sort Value:
- 2020-0111-2020-0000
- Page Start:
- Page End:
- Publication Date:
- 2021-01
- Subjects:
- Exact multiplicity -- S-shaped bifurcation curve -- MEMS -- Bistability -- Fold structure -- Bifurcation surface
Applied mathematics -- Periodicals
519.05 - Journal URLs:
- http://www.sciencedirect.com/science/journal/08939659 ↗
http://www.elsevier.com/journals ↗ - DOI:
- 10.1016/j.aml.2020.106688 ↗
- Languages:
- English
- ISSNs:
- 0893-9659
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 1573.880000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 14023.xml