【摘 要】
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In this paper the existence and nonexistence of non-trivial solution for the Cauchy problem of the form ｛ut=div(｜▽u｜p-2▽u)-(σ)/(σ)xibi(u)-uq,u(x,O)=O,(x,t)∈ST
【机 构】
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Department of Mathematics,Huaqiao University,Fujian 362021,China
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In this paper the existence and nonexistence of non-trivial solution for the Cauchy problem of the form ｛ut=div(｜▽u｜p-2▽u)-(σ)/(σ)xibi(u)-uq,u(x,O)=O,(x,t)∈ST=RN×(O,T),x∈RN｛O｝are studied. We assume that ｜b’i(s)｜≤Msm-1, and proved that if P＞2, 0＜q＜p-1+p/N,0≤m＜p-1+p/N, then the problem has a solution;if p＞2, q＞p-1+p/N,O≤m≤q(p+Np-N-1)/p+Np-N, then the problem has no solution;if p＞2,p-1＜q＜p-1+p/N,0≤m＜q, then the problem has a very singular solution;if p＞2,q＞p-1+p/N,rn0＜m＜q-p/2N,then the problem has no very singular solution.We use P.D.E.methods such as regularization,Moser iteration and Imbedding Theorem.
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