Home

Corrector Theory in Random Homogenization of Partial Differential Equations

Wenjia Jing

Title:
Corrector Theory in Random Homogenization of Partial Differential Equations
Author(s):
Jing, Wenjia
Thesis Advisor(s):
Bal, Guillaume
Date:
Type:
Dissertations
Department:
Applied Physics and Applied Mathematics
Permanent URL:
Notes:
Ph.D., Columbia University.
Abstract:
We derive systematically a theory for the correctors in random homogenization of partial differential equations with highly oscillatory coefficients, which arise naturally in many areas of natural sciences and engineering. This corrector theory is of great practical importance in many applications when estimating the random fluctuations in the solution is as important as finding its homogenization limit. This thesis consists of three parts. In the first part, we study some properties of random fields that are useful to control corrector in homogenization of PDE. These random fields mostly have parameters in multi-dimensional Euclidean spaces. In the second part, we derive a corrector theory systematically that works in general for linear partial differential equations, with random coefficients appearing in their zero-order, i.e., non-differential, terms. The derivation is a combination of the studies of random fields and applications of PDE theory. In the third part of this thesis, we derive a framework of analyzing multiscale numerical algorithms that are widely used to approximate homogenization, to test if they succeed in capturing the limiting corrector predicted by the theory.
Subject(s):
Mathematics
Applied mathematics
Item views:
482
Metadata:
text | xml

In Partnership with the Center for Digital Research and Scholarship at Columbia University Libraries/Information Services | Terms of Use