Simultaneous Versus Nonsimultaneous Blow-up In A Doubly Coupled Nonlinear Parabolic System

In this paper, we study the doubly coupled nonlinear parabolic system Where the parameters l11, l12,l21,l22,p1,p2> 0,0< uo(x),vo(x)∈CI(BR) radially sym-metric and nondecreasing.77 is the outside normal vector on (?)BR, The main con-clusions we get there, u,u are simultaneous blow-up if and only if Q1,Q2≥0, where Q1= max{l12+1-l22,2p1+1-l22}, Q2=max{l21+1-l11,2p2+1-l11}.The simultaneous blow-up rate are when internal source dominant. when boundary flux dominant. when cross dominant.In the introduction, we give the background to the coupled nonlinear parabolic equa-tion. In Chapter 2, we give some basic knowledge to be used in this paper. In Chapter 3, we describe the main results of the paper, and then prove them in Chapter 4. In the last chapter, we give a discussion of the conclusions.