Non-simultaneous Blow-up In Multi-componential Parabolic Equations With Nonlinear Boundary Flux

The nonlinear parabolic equations coming from population dynamics,physics and chemistry show the point-wise phenomena,which owe more important theoretical and application value than the linear parabolic problems.In this paper,we study a class of Neumann initial-boundary problem of parabolic equations,where the solution contains multiple components.The nonlinear terms lead to the singularity of solutions.And three are lots of known and interesting phenomena about singular solutions.For example,any components of the singular solution blow up at the same time;For suitable initial data,the simultaneous and nonsimultaneous blow-up coexist;The different initial data lead to different asymptotic behavior of blow-up solutions.In this thesis,we use the Comparison Principle and Fundamental Solution Methods to deal with the critical blow-up exponent of solutions,the criteria on the simultaneous and nonsimultaneous blow-up of different components.Especially,for the two blow-up components,we obtain three different blow-up classification and blow-up rates also.The paper is arranged as follows: in the first chapter,we present the history of the nonsimultaneous blow-up in nonlinear parabolic equations as well as the main model and related assumptions.In the second chapter,we give the main results and the corresponding proof,including:(1)The sufficient and necessary conditions for at least two components of the solutions blowing up simultaneously;(2)only two components blow up at the same time with the others remain bounded.The blow-up rates are also given;(3)blow-up set.