کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898566 | 1631490 | 2018 | 45 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Homogenization of generalized second-order elliptic difference operators
ترجمه فارسی عنوان
همگن سازی اپراتورهای اختلاف بیضوی دوم مرتبه دوم
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
Consider a function W(x1,â¦,xd)=âk=1dWk(xk), where each Wk:RâR is a strictly increasing right continuous function with left limits. Given a matrix function A=diag{a1,â¦,ad}, let âAâW=âk=1dâxk(akâWk) be a generalized second-order differential operator. Our chief goal is to study the homogenization of generalized second-order difference operators, that is, we are interested in the convergence of the sequence of solutions ofλuNââNANâWNuN=fN to the solution ofλuââAâWu=f, where the superscript N stands for some sort of discretization. In the continuous case we study the problem in the context of W-Sobolev spaces, whereas in the discrete case we develop the theoretical context in the present paper. The main result is a homogenization result. Under minor assumptions regarding weak convergence and ellipticity of these matrices AN, we show that every such sequence admits a homogenization. We provide two examples of matrix functions verifying these assumptions: the first one consists of fixing a matrix function A under minor regularity assumptions, and taking a convenient discretization AN; the second one consists on the case where AN represents a random environment associated to an ergodic group, a case in which we then show that the homogenized matrix A does not depend on the realization Ï of the environment. Finally, we provide an application geared towards the hydrodynamical limit of certain gradient processes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 8, 15 October 2018, Pages 3709-3753
Journal: Journal of Differential Equations - Volume 265, Issue 8, 15 October 2018, Pages 3709-3753
نویسندگان
Alexandre B. Simas, Fábio J. Valentim,