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Pregled bibliografske jedinice broj: 404459

Zbornik radova

Autori: Antonić, Nenad; Vrdoljak, Marko
Naslov: Small-amplitude homogenisation of parabolic problems
Izvornik: Scaling Up for Modeling Transport and Flow in Porous Media, Book of abstracts / B. Amaziane, A. Ern, O. Gipouloux, M. Jurak, M. Kern, E. Marušić-Paloka, I. Mortazavi, R. Tapiero (ur.). -
Skup: Scaling Up for Modeling Transport and Flow in Porous Media
Mjesto i datum: Dubrovnik, Hrvatska, 13-16.10.2008.
Ključne riječi: H-convergence; small-amplitude homogenisation; diffusion equation; H-measure
Sažetak:
Abstract theory of non-periodic homogenisation for non-stationary diffusion equation is much less known than the corresponding theory for stationary iffusion. However, the main results of G-convergence and H-convergence were already obtained by Sergio Spagnolo in the seventies, with some extensions by Vasilij V. Zikov and collaborators in the eighties, and Andrea Dell'Aglio and Francois Murat in the nineties cWe shall prove that the smoothness (with respect to a parameter) is preserved in the process of taking the H-limit, which is essential for our purposes. The small-amplitude homogenisation consists in taking a sequence of coefficients which difference is proportional to a small parameter, and then computing the first correction in the limit. The explicit formula for the correction in the elliptic case can in general be obtained by using H-measures, a tool introduced arround 1990 by Luc Tartar and Patrick Gerard. For parabolic problems, those classical H-measures are not well suited. Recently, the first author (jointly with Martin Lazar) introduced several parabolic variants, which allowed a number of applications to be extended from elliptic to parabolic equations. By using such a variant of H-measures we were able to write the explicit expression for the correction in the parabolic case.
Vrsta sudjelovanja: Predavanje
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Nema recenziju
Projekt / tema: 037-0372787-2795, 037-1193086-3226
Izvorni jezik: ENG
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Upisao u CROSBI: nenad@math.hr (nenad@math.hr), 5. Lip. 2009. u 18:06 sati



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