G-Convergence and Homogenization of Nonlinear Partial Differential Operators (Mathematics and Its Applications, 422)
ISBN-13:
9780792347200
ISBN-10:
079234720X
Edition:
1997
Author:
A.A. Pankov
Publication date:
1997
Publisher:
Springer
Format:
Hardcover
271 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
,
Pure Mathematics
,
Schools & Teaching
FREE US shipping
Book details
ISBN-13:
9780792347200
ISBN-10:
079234720X
Edition:
1997
Author:
A.A. Pankov
Publication date:
1997
Publisher:
Springer
Format:
Hardcover
271 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
,
Pure Mathematics
,
Schools & Teaching
Summary
G-Convergence and Homogenization of Nonlinear Partial Differential Operators (Mathematics and Its Applications, 422) (ISBN-13: 9780792347200 and ISBN-10: 079234720X), written by authors
A.A. Pankov, was published by Springer in 1997.
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Description
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.
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