Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Waurick, Marcus
Affiliations: Institut für Analysis, Fachrichtung Mathematik, Technische Universität Dresden, Dresden, Germany. E-mail: marcus.waurick@tu-dresden.de
Abstract: We present a unified Hilbert space perspective to homogenization of a class of evolutionary equations of mathematical physics. We formulate homogenization in a purely operator-theoretic setting. Using “A structural observation for linear material laws in classical mathematical physics” by R. Picard [Mathematical Methods in the Applied Sciences 32 (2009), 1768–1803], we discuss constitutive relations as certain elements of the Hardy space ℋ∞(E;L(H)) of bounded, analytic and operator-valued functions M:E→L(H), where E\subseteqq C open, H Hilbert space. The core idea is to introduce a certain topology on the set of constitutive relations. Given a convergent sequence of constitutive relations, the behavior of solutions to the respective problems is discussed. We apply the results to the equations of acoustics, thermodynamics, elasticity or coupled systems such as thermo-elasticity. The respective equations may also incorporate memory or delay terms and fractional derivatives. In particular, constitutive relations via differential equations can also be treated.
Keywords: homogenization, evolutionary differential equations, delay and memory effects, fractional derivatives, thermo-elasticity
DOI: 10.3233/ASY-2012-1145
Journal: Asymptotic Analysis, vol. 82, no. 3-4, pp. 271-294, 2013
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl