Fujita Phenomenon In Two Kinds Of Fast Diffusion Systems

In this paper, we mainly consider Fujita phenomenons in two types of fast diffusion systems. We will use the comparison principle and choose proper test functions to get our conclusions that both equation systems will blow-up in finite time. First, we will introduce the history of Fujita exponents, and introduce the comparison principle and something useful for our prove. And then, we will prove those fast diffusion systems ut= ?um+ vp+f1(x, t), vt= ?vn+ uq+ f2(x, t) and ut= ?um+ vp+ f1(x, t, u), vt= ?vn+ uq+ f2(x, t, v)will blow-up in finite time, and get their Fujita exponents.