Global And Blow-Up Solutions Of Several Types Of Nonlinear Parabolic Equations

In this paper, the global and blow-up solutions of several types of nonlinear parabol-ic equations are investigated. By constructing auxiliary functions and using the maximum principle, we obtain the sufficient conditions for the existence of global and blow-up solutions with some appropriate assumptions. The upper estimate of the global solution and the up-per bound for "blow-up time" are also provided. The new results extend and improve some findings in the relevant literatures. The overall structure of this paper is as follows:In Chapter 1, introduction, the background of the discussed problems, the meaning of our study in this paper and the present situation in domestic and foreign research. Meanwhile, the main works of this paper are stated in detail.In Chapter 2, we study the global and blow-up solutions for a type of nonlinear reaction equations. Under suitable assumptions, we obtain the sufficient conditions for the existence of global and blow-up solutions with some appropriate assumptions. The upper estimate of the global solution and the upper bound for "blow-up time" are also provided. By theoretical derivation and simulation, The correctness of the conclusion is validated.In Chapter 3, the global and blow-up solutions for a type of nonlinear parabolic equations with gradient terms under the Neumann boundary condition is investigated. The new results extend and improve some findings in the relevant literatures.In Chapter 4, the global and blow-up solutions for another type of nonlinear parabolic equations with gradient terms and boundary fluxes term is investigated. The global existence and finite time blow-up of positive solutions are obtained, by constructing auxiliary functions and using the maximum principle. Some real examples are given.