Year

2017

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

This work is presented in two parts. In Part I, we focus on the Monge-Ampere type equations and their applications.

In Part II, we achieve regularity results for the Cauchy problems of heat equations driven by a separable inhomogeneous term or a nonseparable general term. As an application, the existence and uniqueness of solutions to the Cauchy problems are arrived. In addition, the results in Part II are applied to obtain pathwise estimates for the heat equation driven by a fractional Brownian sheet.

This thesis is unavailable until Monday, March 16, 2020

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