| 带非局部源的退化半线性抛物方程的解的爆破性质 |
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| 引用本文： | 陈友朋,刘其林,谢春红. 带非局部源的退化半线性抛物方程的解的爆破性质[J]. 高校应用数学学报(英文版), 2002, 17(4): 413-424. DOI: 10.1007/s11766-996-0005-4 |
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| 作者姓名： | 陈友朋 刘其林 谢春红 |
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| 作者单位： | Dept. of Math., Nanjing Univ.,Nanjing 210093,China |
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| 摘 要： |
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| 关 键 词： | 非局部源 退化 半线性抛物方程 方程解 爆破性 |
| 收稿时间： | 2002-04-01 |
The blow-up properties for a degenerate semilinear parabolic equation with nonlocal source |
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| Youpeng Chen,Qilin Liu,Chunhong Xie. The blow-up properties for a degenerate semilinear parabolic equation with nonlocal source[J]. Applied Mathematics A Journal of Chinese Universities, 2002, 17(4): 413-424. DOI: 10.1007/s11766-996-0005-4 |
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| Authors: | Youpeng Chen Qilin Liu Chunhong Xie |
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| Affiliation: | (1) Dept. of Math., Nanjing Univ., 210093 Nanjing, China |
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| Abstract: | This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t − (x a u x ) x =∫ 0 a f(u)dx in (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)=u p , p>1. |
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| Keywords: | 35A07 35B40 35K57 35K60 35K65 |
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