Mathematics and Its Applications

G-Convergence and Homogenization of Nonlinear Partial Differential Operators

Authors: Pankov, A.A.

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About this book

Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-94-015-8957-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-7923-4720-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $169.99
price for USA in USD
  • ISBN 978-90-481-4900-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
G-Convergence and Homogenization of Nonlinear Partial Differential Operators
Authors
Series Title
Mathematics and Its Applications
Series Volume
422
Copyright
1997
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8957-4
DOI
10.1007/978-94-015-8957-4
Hardcover ISBN
978-0-7923-4720-0
Softcover ISBN
978-90-481-4900-1
Edition Number
1
Number of Pages
XIII, 258
Topics