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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS

Publisher: 
American Mathematical Society/Courant Institute of Mathematical Sciences
Number of Pages: 
318
Price: 
50.00
ISBN: 
9780821849576
Date Received: 
Tuesday, May 4, 2010
Reviewable: 
No
Include In BLL Rating: 
No
Reviewer Email Address: 
Pierpaolo Esposito, Nassif Ghoussoub, and Yujin Guo
Series: 
Courant Lecture Notes 20
Publication Date: 
2010
Format: 
Paperback
Category: 
Monograph
  • Introduction

Part 1. Second-order equations modeling stationary MEMS

  • Estimates for the pull-in voltage
  • The branch of stable solutions
  • Estimates for the pull-in distance
  • The first branch of unstable solutions
  • Description of the global set of solutions
  • Power-law profiles on symmetric domains

Part 2. Parabolic equations modeling MEMS dynamic deflections

  • Different modes of dynamic deflection
  • Estimates on quenching times
  • Refined profile of solutions at quenching time

Part 3. Fourth-order equations modeling nonelastic MEMS

  • A fourth-order model with a clamped boundary on a ball
  • A fourth-order model with a pinned boundary on convex domains
  • Appendix A. Hardy-Rellich inequalities
  • Bibliography
  • Index
Publish Book: 
Modify Date: 
Tuesday, May 4, 2010

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