Blow-up Time Of The Solutions For Serval Classes Of Parabolic Equations

In this paper, we consider the bounds for the blowup time of a class of quasi-linear parabolic equation and that of a system of parabolic equations with nonlocalfactors in nonlinearities.The paper can be divided into four chapters.In Chapter1, we introduce the background of these problems and the cur-rent situation in this direction. We also list the results of this thesis and itsconstruction.In Chapter2, we consider a class of quasi-linear parabolic equation subjectto boundary condition and initial value. Following the methods of Payne andSchaefer’s, we obtain the lower bound for the blowup time of the solution to theproblem, which is the first result in this direction which is about the lower boundfor the blowup time in the higher dimension. Meanwhile, we also give the estimatefor the upper bound of the blowup time. In the special cases, we even get theaccurate value of the blowup time.In Chapter3, we deal with a system of parabolic equations with nonlocalfactors subject to boundary conditions and initial data. Through delicate analysistechnique and using some inequalities, we get the lower and upper bounds for theblowup time.In Chapter4, we give the review and summarization of this thesis, we pointout some open problems which can be given deepen research in the future.