Blowup Analysis For Solutions To The Quasilinear Parabolic Equation And A System Of Parabolic Equations With Nonlocal Nonlinearities

In this paper, we mainly study the bounds for the blowup time and blowup rate of solutions to the quasilinear parabolic equation and a system of parabolic equations with nonlocal nonlinearities.The paper can be divided into five chapters.In the first chapter, We introduce the background and current situation of the problems and the structure of this paper.In the second chapter, we mainly introduce the preliminary knowledge.The third chapter is concerned with bounds for the blowup time and blowup rate of the quasilinear parabolic equation when space dimensions are one and two, making up for the deficiency of the existing work in low dimension cases. In addition we respectively use different ways to get the bounds for the blowup time and blowup rate.In the fourth chapter, we focus on the bounds for the blowup time of the solution to a system of parabolic equations with nonlocal nonlinearities. According to different space dimension, we use different methods to get the lower bounds for the blowup time and construct the lower solution to get the upper bound for the blowup time. In particular, when space dimension n? 3, the method which we use is novel and unique. Finally, we discuss the phenomenon of nonsimultaneous blowup.The last chapter is a conclusion and outlook. We summarize the thesis and give some open problems.