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.
Recommended Citation
Li, Siyuan, Monge–Ampère type equations and their applications and heat equations driven by irregular terms, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2017. https://ro.uow.edu.au/theses1/211
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.