Blow-up Of Solutions To A Class Of Nonlinear Parabolic Equations With Special Diffusion Coefficients

In this paper,we consider the blow-up properties of solutions of a class of nonlinear parabolic equations with special diffusion coefficients where ?(?)Rn(n? 3)is a bounded domain with a smooth boundary(?)?,0??,?pu=div(|?u|p-2?u),2<p<n,0?u0?W01,p(?),u0(x)(?)0.In addition,forx=(x1,x2,…,xn)?Rn,|x|=(?).The weight function k(t)and the nonlinear function f satisfy the following assumptions:(?)k ? C1[0,+?),k(0)>0,k(t)? 0,?t ?[0,+?);(?)sf(s)?0,(?)s ? R;(?)f ? C1(R)and there exists a constant q>1 such that sf(s)?(q+1)F(s),(?)s?R;(?)There exist constants a,b>0 and q ?(1,p*-1)such that|f(s)| ? a+b|s|q,(?)s ? R.Here p*=np/n-p for n>p and p*=? for n?p.At first,the research background and current research status of nonlinear parabolic e-solution to problem(0.1)that blows up at T.Then T?:L1-?(0)/C*(?-1),where L(0)=1/2?u0/|x|?22,?>1 and C*>0 are constants depending on n,p and q.