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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS
About this Title
Pierpaolo Esposito, Università degli Studi Roma Tre, Rome, Italy, Nassif Ghoussoub, University of British Columbia, Vancouver, BC, Canada and Yujin Guo, University of Minnesota, Minneapolis, MN
Publication: Courant Lecture Notes
Publication Year:
2010; Volume 20
ISBNs: 978-0-8218-4957-6 (print); 978-1-4704-1763-5 (online)
DOI: https://doi.org/10.1090/cln/020
MathSciNet review: MR2604963
MSC: Primary 35-02; Secondary 47J15, 74F15, 74K15, 74M05, 78A30
Table of Contents
Front/Back Matter
Chapters
- Chapter 1. Introduction
Second-order equations modeling stationary MEMS
- Chapter 2. Estimates for the pull-in voltage
- Chapter 3. The branch of stable solutions
- Chapter 4. Estimates for the pull-in distance
- Chapter 5. The first branch of unstable solutions
- Chapter 6. Description of the global set of solutions
- Chapter 7. Power-law profiles on symmetric domains
Part 2. Parabolic equations modeling MEMS dynamic deflections
- Chapter 8. Different modes of dynamic deflection
- Chapter 9. Estimates on quenching times
- Chapter 10. Refined profile of solutions at quenching time
Part 3. Fourth-order equations modeling nonelastic MEMS
- Chapter 11. A fourth-order model with a clamped boundary on a ball
- Chapter 12. A fourth-order model with a pinned boundary on convex domains
- Appendix A. Hardy–Rellich inequalities