Study On The Global Existence And Finite Time Blow-up For Two Classes Of Nonlinear Parabolic System With Nonlocal Source

In this dissertation,we consider global existence and finite time blow-up for two classes of nonlinear parabolic system.Firstly,we study the blow-up of solutions to a parabolic system with nonlocal source,we get the conditions on global existence,simultaneous or non-simultaneous blow-up,blow-up set,uniform blow-up profiles and boundary layer are got by using comparison principle and asymptotic analysis methods.Then we consider the global existence and finite time blow-up for a class of thin-film equation,on the base of[Global existence blow up and extinction for a class of thin-film equation,Nonlinear Analysis:Theory Methods and Applications,147:96-109,2016]by Li,Gao and Han,firstly,we consider the upper and lower bounds of blow-up time and asymptotic behavior when J?u₀?<E1 and J?u₀?<d respectively,and also study the asymptotic behavior of the solutions;secondly,we study the conditions on global existence or blow-up when J?u₀?>d.There are three chapters in this dissertation:In the first chapter,we mainly introduce the current researches about the global existence and blowup of solutions to nonlinear parabolic equations,as well as the purposes,the innovations and the methods of this dissertation.In the second chapter,we study the blow-up of solutions to a parabolic system with nonlocal source.In this chapter,we not only give the conditions on global,simultaneous or non-simultaneous blow-up,but also get the blow-up set,uniform blow-up profiles and boundary layer by using comparison principle and asymptotic analysis methods.In the third chapter,we continue to study the global existence and finite time blow-up for a class of thin-film equation.We mainly considers the two questions:firstly,we consider the upper and lower bounds of blow-up time and asymptotic behavior when J?u₀?<d;secondly,we study the conditions on global existence or blow-up when J?u₀?>d.