The type of problem under consideration is{ut = (△)(a(u)b(x)(△)u) + g(x,q,t)f(u)in D(0,T),u=0onГ1×(0,T), (e)u/(e)u+ +σ(x,t)u = 0 on Г2×(0,T),Г1∪Г2=(e)D, u(x,0) = uo(x) ≥ 0,(≠) 0 in(￣D),where D is a smooth bounded domain of RN,q=｜(△)u｜2.By constructing an auxiliary function and using Hopf's maximum principles on it,existence theorems of blow-up solutions,upper bound of “blow-up time” and upper estimates of “blow-up rate” axe given under suitable assumptions on a,b,f,g,σ and initial date uo(x).The obtained results are applied to some examples in which a,b,f,g and σ are power functions or exponential functions.
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