Semilinear parabolic equation in RN associated with critical Sobolev exponent
Semilinear parabolic equation in RN associated with critical Sobolev exponent
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DOI：
10.1016/j.anihpc.2010.01.002
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发表时间：
2010-05
影响因子：
1.9
通讯作者：
R. Ikehata;M. Ishiwata;Takashi Suzuki
中科院分区：
文献类型：
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作者：
R. Ikehata;M. Ishiwata;Takashi Suzuki
我们考虑整个空间 RN, N⩾3 上的半线性抛物线方程 ut−Δu=|u|p−1u，其中指数 p=(N+2)/(N−2) 与 Sobolev 嵌入 H1(RN)⊂Lp+1(RN) 相关。首先，我们通过势阱和前向自相似变换研究解的衰减和爆炸。然后，我们讨论无限时间内的爆炸并对轨道进行分类。
We consider the semilinear parabolic equation ut−Δu=|u|p−1u on the whole space RN, N⩾3, where the exponent p=(N+2)/(N−2) is associated with the Sobolev imbedding H1(RN)⊂Lp+1(RN). First, we study the decay and blow-up of the solution by means of the potential-well and forward self-similar transformation. Then, we discuss blow-up in infinite time and classify the orbit.