The Upper And Lower Bound Estimates On The Blow-up Time Of The Solutions For Two Classes Of Nonlinear Parabolic Equations With A Gradient Term

The blow-up properties of the solutions for nonlinear parabolic equations areimportant aspects of partial differential equation theory. In Chapter2, we considerglobal existence and blow-up solutions for quasilinear reaction-diffusion equations witha gradient absorption term. Through constructing suitable auxiliary functions and usingmaximum principles, we obtains sufficient condition for the existence of the global andblow-up solution, an upper bound for the blow-up time, an upper estimate of theblow-up rate. In Chapter3, by using the method of energy inequality we derivesufficient conditions for the blow-up solutions of pseudo-parabolic equations and theupper and lower bound estimates on the blow-up time for the solution.