A.A. Pankov G-Convergence and Homogenization of Nonlinear Partial Differential Operators 9789048149001

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Автор: A.A. Pankov
Название: G-Convergence and Homogenization of Nonlinear Partial Differential Operators
ISBN: 9789048149001
Издательство: Springer
Классификация: ISBN-10: 9048149002
Обложка/Формат: Paperback
Страницы: 258
Вес: 0.39 кг.
Дата издания: 08.12.2010
Серия: Mathematics and Its Applications
Язык: English
Размер: 234 x 156 x 15
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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.

G-Convergence and Homogenization of Nonlinear Partial Differential Operators, A.A. Pankov