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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (Courant Lecture Notes in Mathematics, Band 20) - Softcover

Esposito, Pierpaolo; Ghoussoub, Nassif; Guo, Yujin

 
9780821849576: Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (Courant Lecture Notes in Mathematics, Band 20)
Softcover
ISBN 10: 0821849573 ISBN 13: 9780821849576
Verlag: American Mathematical Society, 2010

Inhaltsangabe

Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing 'electrostatically actuated' MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems - where the stationary MEMS models fit - are a well-developed field of PDEs, the type of inverse square nonlinearity that appears here helps shed a new light on the class of singular supercritical problems and their specific challenges. Besides the practical considerations, the model is a rich source of interesting mathematical phenomena. Numerics, formal asymptotic analysis, and ODE methods give lots of information and point to many conjectures. However, even in the simplest idealized versions of electrostatic MEMS, one essentially needs the full available arsenal of modern PDE techniques to do the required rigorous mathematical analysis, which is the main objective of this volume. This monograph could therefore be used as an advanced graduate text for a motivational introduction to many recent methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance.

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Über die Autorin bzw. den Autor

Pierpaolo Esposito, Università degli Studi Roma Tre, Rome, Italy

Nassif Ghoussoub, University of British Columbia, Vancouver, BC, Canada

Yujin Guo, University of Minnesota, Minneapolis, MN, USA

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Verlag
American Mathematical Society
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
0821849573
ISBN 13 
9780821849576
Einband
Taschenbuch
Anzahl der Seiten
318
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