Blowup Analysis For The Solution To Some Types Of Parabolic Equations

In this paper, we mainly study the bounds for the blowup time and blowuprate of the solution to some types of parabolic equation with weighted source. Wealso consider the relationships between PDE and ODE as well as their applications.The paper can be divided into five chapters.The first chapter is the introduction of the whole paper. We introduce thebackground and current situation of the problems, preliminary knowledge andstructure of this paper.The second chapter is concerned with a problem of parabolic equation withweighted nonlinear source subject to boundary condition and initial value. Underdiferent conditions, we use diferent methods to get the upper and lower boundsfor the blowup time and blowup rate.In the third chapter, we focus on the bounds for the blowup time of thesolution to parabolic equation with weighted source subject to nonhomogeneousNeumann boundary condition in R3.The relationship between PDE and ODE is given in the fourth chapter.Roughly, through the space-time integration of the partial diferential equation,we can change it into a problem of ODE, then we can obtain the blowup time andblowup rate.The last chapter is a conclusion and outlook. We summarize the thesis andgive some open problems.