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Mathematical analysis of partial dif...

Ghoussoub, N. (1953-)

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Mathematical analysis of partial differential equations modeling electrostatic MEMS /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematical analysis of partial differential equations modeling electrostatic MEMS // Pierpaolo Esposito, Nassif Ghoussoub, Yujin Guo.
作者:	Esposito, Pierpaolo.
其他作者:	Ghoussoub, N.
出版者:	Providence, R.I. :American Mathematical Society, : 2010.,
面頁冊數:	xiii, 318 p. :ill. ;26 cm.
標題:	Microelectromechanical systems - Mathematical models. -
ISBN:	9780821849576 (pbk.) :

Mathematical analysis of partial differential equations modeling electrostatic MEMS /
Esposito, Pierpaolo.

Mathematical analysis of partial differential equations modeling electrostatic MEMS /Pierpaolo Esposito, Nassif Ghoussoub, Yujin Guo. - Providence, R.I. :American Mathematical Society,2010. - xiii, 318 p. :ill. ;26 cm. - Courant lecture notes in mathematics ;20. - Courant lecture notes in mathematics ;20..

Includes bibliographical references (p. 309-215) and index.

"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."--Publisher's description.

ISBN: 9780821849576 (pbk.) :US46.50

LCCN: 2009045518Subjects--Topical Terms:

1083998
Microelectromechanical systems
--Mathematical models.

LC Class. No.: TK7875 / .M385 2010

Mathematical analysis of partial differential equations modeling electrostatic MEMS /
LDR:02290cam 2200217 a 4500 001 903948
003 OCoLC
005 20101130092838.0
008 101126s2010 riua b 001 0 eng
010 $a 2009045518
020 $a 9780821849576 (pbk.) : $c US46.50
020 $a 0821849573 (pbk.)
035 $a (OCoLC)466771715
035 $a AS99TN09050
040 $a DLC $c DLC $d YDX $d YDXCP $d UBY $d CDX $d UV0 $d WAU $d NDHU
050 0 0 $a TK7875 $b .M385 2010
100 1 $a Esposito, Pierpaolo. $3 1083997
245 0 0 $a Mathematical analysis of partial differential equations modeling electrostatic MEMS / $c Pierpaolo Esposito, Nassif Ghoussoub, Yujin Guo.
260 $a Providence, R.I. : $c 2010. $b American Mathematical Society,
300 $a xiii, 318 p. : $b ill. ; $c 26 cm.
490 1 $a Courant lecture notes in mathematics ; $v 20
504 $a Includes bibliographical references (p. 309-215) and index.
520 $a "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."--Publisher's description.
650 0 $a Microelectromechanical systems $x Mathematical models. $3 1083998
650 0 $a Mathematical analysis. $3 516833
700 1 $a Ghoussoub, N. $q (Nassif), $d 1953- $3 672099
700 1 $a Guo, Yujin. $3 1083996
830 0 $a Courant lecture notes in mathematics ; $v 20. $3 1083999