dc.creator | Liao, Naian | |
dc.date.accessioned | 2020-08-22T00:44:34Z | |
dc.date.available | 2014-05-27 | |
dc.date.issued | 2014-05-27 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-05202014-220122 | |
dc.identifier.uri | http://hdl.handle.net/1803/12346 | |
dc.description.abstract | In this thesis, we prove the existence of solutions to the Dirichlet problem
for a logarithmic diffusion
equation can be established when the boundary datum satisfies a certain condition.
We also show that if the boundary datum vanishes on an open subset of the side boundary then
solutions in general do not exist. We present several local regularity properties
of solutions to the logarithmic diffusion equation under certain assumptions
including a Harnack-type inequality,
the local analyticity of solutions,
and an $L^1_{loc}$-type Harnack inequality.
We also use the Harnack-type inequality to establish a
topology by which local solutions to the porous medium equations
converge to solutions to the logarithmic diffusion equation.
The conclusions are examined and discussed in a series of examples and counter-examples. | |
dc.format.mimetype | application/pdf | |
dc.subject | local behaviors | |
dc.subject | existence | |
dc.subject | singular equation | |
dc.title | Topics on a Logarithmic Diffusion Equation | |
dc.type | dissertation | |
dc.contributor.committeeMember | Dechao Zheng | |
dc.contributor.committeeMember | Larry Schumaker | |
dc.contributor.committeeMember | Anne Kenworthy | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2014-05-27 | |
local.embargo.lift | 2014-05-27 | |
dc.contributor.committeeChair | Emmanuele DiBenedetto | |