Parabolic equations without a minimum principle

In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and existence of the solution for initial data, which may not be continuous at two boundary points. We also examine the circumstances when these solutions admit a probabilistic interpretation. Some partial results are given for analogous problems in more than one dimension.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Pang, Huadong

Advisor dc:contributor.advisor

• Daniel Stroock.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/38958

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38958