Laplace's equation, the nonlinear Poisson equation and the effects of Gaussian white noise on the boundary

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Publication Type dissertation
School or College College of Science
Department Mathematics
Author Khader, Karim
Title Laplace's equation, the nonlinear Poisson equation and the effects of Gaussian white noise on the boundary
Date 2010-05
Description Elliptic partial differential equations (PDE's) and corresponding boundary value problems are well understood with a variety of boundary data. Over the past 25 years, an abundance of research has been done in stochastic PDE's (SPDE's), with an emphasis on equations having a time parameter on domains with low spatial dimension and whose boundary is smooth. The meaning of a solution to a class of elliptic SPDE's on a domain D C Rd, d ? 2 with Lipschitz boundary ?D is described. For this class of SPDE's, the randomness appears as a Gaussian white noise on the boundary of the domain. Existence, uniqueness and regularity results are obtained, and it is shown that these solutions are almost surely classical. For the Laplacian and the Helmholtz operator, the behavior of the solution near the boundary of the unit ball is described and in the case of the Laplacian, the solution is simply the harmonic extension of white noise and so many of the well-known properties of harmonic functions hold.
Type Text
Publisher University of Utah
Subject Laplace's equation; Poisson equation; Gaussian white noise
Subject LCSH Boundary value problems; Differential equations, Elliptic
Dissertation Institution University of Utah
Dissertation Name PhD
Language eng
Rights Management ©Karim Khader
Format Medium application/pdf
Format Extent 503,711 bytes
Identifier us-etd2,151769
Source Original in Marriott Library Special Collections, QA3.5 2010 .K43
ARK ark:/87278/s6cc1f65
Setname ir_etd
Date Created 2012-04-23
Date Modified 2017-09-26
ID 192647
Reference URL https://collections.lib.utah.edu/ark:/87278/s6cc1f65