Small-amplitude homogenisation of parabolic problems (CROSBI ID 550022)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa
Podaci o odgovornosti
Antonić, Nenad ; Vrdoljak, Marko
engleski
Small-amplitude homogenisation of parabolic problems
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.
H-convergence ; small-amplitude homogenisation ; diffusion equation ; H-measure
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Podaci o prilogu
32-33.
2008.
objavljeno
Podaci o matičnoj publikaciji
Amaziane, B. ; Ern, A. ; Gipouloux, O. ; Jurak, M. ; Kern, M. ; Marušić-Paloka, E. ; Mortazavi, I. ; Tapiero, R.
Podaci o skupu
Scaling Up for Modeling Transport and Flow in Porous Media
predavanje
13.10.2008-16.10.2008
Dubrovnik, Hrvatska