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Courant Lecture Notes
2010; 318 pp; softcover
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Order Code: CLN/20
Optimal Control of Partial Differential Equations: Theory, Methods and Applications - Fredi Troltzsch
Differential Equations, Mechanics, and Computation - Richard S Palais and Robert A Palais
Hyperbolic Partial Differential Equations - Peter D Lax
Nassif Ghoussoub is the winner of the 2010 CMS David Borwein Award
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.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Graduate students and research mathematicians interested in PDEs and applications.
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