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11.
Given a subset E of convex functions from
into
which satisfy growth conditions of order p>1 and an open bounded subset
of
, we establish the continuity of a map μΦμ from the set of all Young measures on
equipped with the narrow topology into a set of suitable functionals defined in
and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization. 相似文献
12.
Constantin Năstăsescu Florin Panaite Freddy Van Oystaeyen 《Algebras and Representation Theory》1999,2(3):211-226
We apply to Hopf algebras a construction from graded rings, called the group ring of a graded ring. By using this construction we study the transfer of properties between certain categories of relative Hopf modules. As another application, we obtain a Maschke-type theorem for a Galois extension over a semisimple Hopf algebra. 相似文献
13.
Roman Luis J. Zhang Xinsheng Zheng Weian 《Mathematical Physics, Analysis and Geometry》2003,6(2):113-124
We consider the solutions to /tu
(n)=a
(n)(x)u
(n) where {a
(n)(x)}
n=1,2,... are random fields satisfying a well-mixing condition (which is different to the usual strong mixing condition). In this paper we estimate the rate of convergence of u
(n) to the solution of a heat equation. Since our equation is of simple form, we get quite strong result which covers the previous homogenization results obtained on this equation. 相似文献
14.
We compute the -limit of a sequence obstacle functionals in the case of periodic obstacles. 相似文献
15.
We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction [0, max] (max is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for 0 and an asymptotic solution for max. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data. 相似文献
16.
Several choices of scaling are investigated for a coupled system of parabolic partial differential equations in a two‐phase medium at the microscopic scale. This system may be regarded as modelling a reaction–diffusion problem, the Stokes problem of single‐phase flow of a slightly compressible fluid or as a heat conduction problem (with or without interfacial resistance), for example. It is shown that, starting with the same problem on the microscopic scale, different choices of scaling of the diffusion coefficients (resp. permeability or conductivity) and the interfacial‐exchange coefficient lead to different types of macroscopic systems of equations. The characterization of the limit problems in terms of the scaling parameters constitutes a modelling tool because it allows to determine the right type of limit problem. New macroscopic models, not previously dealt with, arise and, for some scalings, classical macroscopic models are recovered. Using the method of two‐scale convergence, a unified approach yielding rigorous proofs is given covering a very broad class of different scalings. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
本文讨论了δtuε-divA(x/ε,↓Δuε)-kuε=f的整体吸引子A^ε与其均匀化后的方程δtu-divA(↓Δu)-ku=f的整体吸引子A^0之间的关系,并给出了A^ε与A^0之间距离的估计。 相似文献
18.
Summary In this contribution, the mechanical behaviour of different ZrO2/NiCr 80 20 compositions is analysed and compared with experimental findings. The microwave-sintered material is found to
possess a slightly dominant ceramic matrix for intermediate volume fractions. Its thermal expansion coefficient deviates from
the rule of mixture. The modulus and the stress strain behaviour can be simulated by a numerical homogenization procedure,
and the influence of residual stresses is found to be negligible. A newly introduced parameter (matricity) describes the mutual
circumvention of the phases and is found to strongly control the stress level of the composite, globally as well as locally.
Finally, a graded component and a metal/ceramic bi-material are compared for thermal as well as mechanical loading.
Received 23 November 1999; accepted for publication 26 May 2000 相似文献
19.
Andrii Khrabustovskyi Holger Stephan 《Mathematical Methods in the Applied Sciences》2008,31(15):1809-1834
We consider a general linear reaction–diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle and positivity of the solution and investigate its asymptotic behavior. Moreover, we give an explicit expression of the limit of the solution for large times. In order to obtain these results, we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution to a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction–diffusion system. Using this and the facts that the diffusion equation on manifolds satisfies the maximum principle and its solution converges to a easily calculated constant, we can obtain analogous properties for the original system. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
20.
The heterogeneous multiscale method (HMM) is applied to various parabolic problems with multiscale coefficients. These problems can be either linear or nonlinear. Optimal estimates are proved for the error between the HMM solution and the homogenized solution.