Fractional Diffusion in Gaussian Noisy Environment

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Issue Date
2015-12-31Author
Hu, Guannan
Publisher
University of Kansas
Format
121 pages
Type
Dissertation
Degree Level
Ph.D.
Discipline
Mathematics
Rights
Copyright held by the author.
Metadata
Show full item recordAbstract
Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel.
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