کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592025 1335069 2008 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homogenization of periodic linear degenerate PDEs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Homogenization of periodic linear degenerate PDEs
چکیده انگلیسی

It is well known under the name of ‘periodic homogenization’ that, under a centering condition of the drift, a periodic diffusion process on Rd converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of this result all rely on uniform ellipticity or hypoellipticity assumptions on the diffusion. In this paper, we considerably weaken these assumptions in order to allow for the diffusion coefficient to even vanish on an open set. As a consequence, it is no longer the case that the effective diffusivity matrix is necessarily non-degenerate. It turns out that, provided that some very weak regularity conditions are met, the range of the effective diffusivity matrix can be read off the shape of the support of the invariant measure for the periodic diffusion. In particular, this gives some easily verifiable conditions for the effective diffusivity matrix to be of full rank. We also discuss the application of our results to the homogenization of a class of elliptic and parabolic PDEs.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 255, Issue 9, 1 November 2008, Pages 2462-2487