Global And Blow-up Solutions Of Parabolic Equations With Multivariable Nonlinear Boundary Flux

The study of blow-up phenomenon of nonlinear parabolic equations is an important part of the theory of partial differential equations.The parabolic equations studied in this paper include nonlinear reaction,nonlinear diffusion,nonlinear convection and nonlinear bound-ary flows.By constructing auxiliary functions,with the aid of differential inequalities,and maximum principle,we study the existence of global solutions and blow-up solutions of some class of nonlinear parabolic equations with nonlinear boundary flux,and the upper estimate of global solution,the upper bound of blow-up time and blow-up rate.In this paper,the boundary flux function studied in this paper is not only affected by the variable u,but also related to the space variable x and the time variable t.The contents of this paper are as followsIn Chapter 1,the background and meaning of the discussed problems and research status at home and abroad of the problems studied in this paper are briefly summarized.And the main work done in this paper is introduced in detailIn Chapter 2,we study the blow-up problem of a class of parabolic equations with nonlinear boundary flux.By constructing appropriate auxiliary functions and utilizing the maximum principle,we solve this problem and obtain sufficient conditions for the existence of global solutions and blow-up solutions.Lastly,some examples are given to verify the correctness of the resultsIn Chapter 3,the global solutions and blow-up solutions of a class of parabolic equations with time variable under nonlinear boundary flux are discussed.Sufficient conditions for the existence of corresponding solutions of the equation are obtained.The upper estimates of global solutions,the upper bounds of blow-up time and blow-up rate are obtained.The results of related literatures are generalized and improvedIn Chapter 4,we study the global existence and blow-up of solutions to the p-Laplacian parabolic equations with gradient terms and nonlinear boundary flux.By constructing an auxiliary function and using the maximum principle,the corresponding conclusions of the global solution and blow-up solution are obtained.Finally,some examples are given.