Academic Commons

Theses Doctoral

Homogenization of Partial Differential Equations with Random, Large Potential

Zhang, Ningyao

Partial differential equations with highly oscillatory, random coefficients describe many applications in applied science and engineering such as porous media and composite materials. Homogenization of PDE states that the solution of the initial model converges to the solution to a macro model, which is characterized by the PDE with homogenized coefficients. Particularly, we study PDEs with a large potential, a class of PDEs with a potential properly scaled such that the limiting equation has a non-trivial (non-zero) potential.
This thesis consists of the investigation of three issues. The first issue is the convergence of Schodinger equation to a deterministic homogenized PDE in high dimension. The second issue is the convergence of the same equation to a stochastic PDE in low dimension. The third issue is the convergence of elliptic equation with an imaginary potential.

Subjects

Files

  • thumnail for Zhang_columbia_0054D_11542.pdf Zhang_columbia_0054D_11542.pdf application/pdf 502 KB Download File

More About This Work

Academic Units
Applied Physics and Applied Mathematics
Thesis Advisors
Bal, Guillaume
Degree
Ph.D., Columbia University
Published Here
September 13, 2013
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.