{"id":{"repo_id":"columbia-diss","oai_identifier":"oai:academiccommons.columbia.edu:10.7916/D88340C0"},"canonical_url":"https://search.dev.ndltd.org/etd/columbia-diss/oai:academiccommons.columbia.edu:10.7916/D88340C0","repository":{"repo_id":"columbia-diss","name":"Columbia University","base_url":"https://academiccommons.columbia.edu/oai"},"display":{"title":"Homogenization of Partial Differential Equations with Random, Large Potential","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Zhang, Ningyao"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T01:44:34Z","subjects":["Mathematics","Differential equations, Partial","Homogenization (Differential equations)"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.7916/D88340C0","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Zhang, Ningyao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013"]},{"key":"dc:type","label":"Dc Type","values":["Theses"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Differential equations, Partial","Homogenization (Differential equations)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7916/D88340C0"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Homogenization of Partial Differential Equations with Random, Large Potential"]}]}],"canonical_facts":{"dc:creator":["Zhang, Ningyao"],"dc:date":["2013"],"dc:description":["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."],"dc:identifier":["https://doi.org/10.7916/D88340C0"],"dc:language":["English"],"dc:subject":["Mathematics","Differential equations, Partial","Homogenization (Differential equations)"],"dc:title":["Homogenization of Partial Differential Equations with Random, Large Potential"],"dc:type":["Theses"]},"updated_at":"2026-07-24T01:44:34Z"}