The blow-up properties for a degenerate semilinear parabolic equation with nonlocal source
The blow-up properties for a degenerate semilinear parabolic equation with nonlocal source
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DOI：
10.1007/s11766-996-0005-4
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发表时间：
2002-12
影响因子：
1
通讯作者：
Chen Youpeng;Liu Qi-lin;Xie Chunhong
中科院分区：
文献类型：
--
作者：
Chen Youpeng;Liu Qi-lin;Xie Chunhong
本文研究齐次狄利克雷条件下非局部简并半线性抛物型方程ut− (xaux)x=∫0af(u)dxin (0,a) × (0,T)正解的爆炸性质。经典解的局部存在性和唯一性成立。在适当的假设下，得到了正解的全局存在性和有限时间内的爆炸性。也证明了爆炸集几乎是整个域。这与当地的情况不同。此外，对于特殊情况，吹胀率是精确确定的：f(u)=up，p>1。
This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equationut− (xaux)x=∫0af(u)dxin (0,a) × (0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow-up in finite time of positve solutions are obtained. It is also proved that the blow-up set is almost the whole domain. This differs from the local case. Furthermore, the blow-up rate is precisely determined for the special case:f(u)=up, p>1.