- Title Information
- Title
- A Derivation and Analysis of the N-point Hierarchy For Conservation Laws And Multistable Dynamics with White Noise in the Allen-Cahn Equation
- Name:
Personal
- Name Part
- Caginalp, Carey
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Dafermos, Constantine
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Kaspar, David
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2017
- Physical Description
- Extent
- xi, 106 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2017
- Genre (aat)
- theses
- Abstract
- The first part of this thesis concerns conservation laws subject to random initial conditions. Using a
discrete set of values for the solution, one can derive a hierarchy of equations in terms of the states.
This hierarchy involves the n-point function, the probability that the solution takes on various
values at different positions, in terms the n+1-point function. A second approach involves obtaining
statistics on the n-point function with shocks. This approach yields a hierarchy of equations in
which the time derivative of the n-point function is expressed in terms of the spatial derivatives of
the n+1 and lower functions. The hierarchy of equations remains valid through collisions of shocks.
In the second part of this thesis, we study the influence of multistable dynamics under the influence
of white noise in a model of an ODE with a cubic nonlinearity. A prototypical bistable dynamic is
replaced by white noise to obtain a stochastic di¤erential equation. A key question is whether there
is a steady state, or invariant measure, and if so, what form it takes. We show that under the limit
of a vanishing amount of this white noise, there is indeed an invariant measure concentrated as a
Dirac type measure at the most stable equilibria if fluctations are uniform, or at multiple equilibria
if they are not.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00893484")
- Topic
- Differential equations, Partial
- Subject
- Topic
- Stochastics
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01077737")
- Topic
- Probabilities
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20170616
- Identifier:
DOI
- 10.7301/Z0N014ZJ
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations