作者：LIU; Wei-ling; LI; Guo-fu非线性边界条件非线性抛物型方程组爆破速率估计边值问题
摘要：In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered:{ut=uxx+ul11vl12,vt=uxx+ul21vl22,(x,t)∈(0,1)(×)(0,T),ux(0,t)=0,vx(0,t)=0,t∈(0,T),ux(1,t)=(up11vp12)(1,t),vx(1,t)=(up21vp22)(1,t),t∈(0,T),u(x,0)=u0(x)1v(x,0)=v0(x),x∈(0,1).We will prove that there exist two positive constants such that: cx∈[0,1] ≤ max u(x,t)(T-t)r/(l1-1)≤C,0 ＜ t ＜ T, c ≤ max x∈[0,1] v(x,t)(T-t)1/(t1-1)≤C,0＜t＜T,where l1 =l2iα/α2 + l22,r = α1/α2 ＞ 1, α1 ≤α2 ＜ 0.
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