Blow-up Time Of The Solutions To Two Nonlinear Evolution Equations

Nonlinear parabolic equation is an important aspect of nonlinear partial differentialequations, so the studying of the existence of the global and blow-up theory of thesolutions for nonlinear evolution equations is a very important direction. In this paper,we will study the blow-up behavior for two kinds of nonlinear evolution equations.In Chapter1, we will state the history of nonlinear parabolic equations and thepresent development situation.In Chapter2, we discuss a class of nonlinear parabolic equation with mixedboundary condition. By constructing some auxiliary functions and combining with therelated theorem, principle, inequality, we get a sufficient condition for the finite timeblow-up and a lower bound for the blow-up time of the solution.In Chapter2, we will study a kind of classic Keller-Segel model. By constructingsome auxiliary functions and using the related theorem, we we get a lower bound for theblow-up time of the solution.