带非局部源的退化奇异半线性抛物方程的爆破 |
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引用本文: | 陈友朋,谢春红. 带非局部源的退化奇异半线性抛物方程的爆破[J]. 数学学报, 2004, 47(1): 41-50. DOI: cnki:ISSN:0583-1431.0.2004-01-005 |
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作者姓名: | 陈友朋 谢春红 |
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作者单位: | 1. 南京师范大学数学与计算机科学院,南京,210097 2. 南京大学数学系,南京,210093 |
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摘 要: | 本文研究带齐次Dirichlet边界条件的非局部退化奇异半线性抛物方程ut-(xαux)x=∫0af(u)dx在(0,a)×(0,T)内正解的爆破性质,建立了古典解的局部存在性与唯一性.在适当的假设条件下,得到了正解的整体存在性与有限时刻爆破的结论.本文还证明了爆破点集是整个区域,这与局部源情形不同.进而,对于特殊情形:f(u)=up,p>1及,f(u)=eu,精确地确定了爆破的速率.
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关 键 词: | 退化奇异抛物方程 非局部源 整体存在 |
文章编号: | 0583-1431(2004)01-0041-10 |
Blow-up for Degenerate and Singular Semilinear Parabolic Equations with Nonlocal Source |
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Affiliation: | You Peng CHEN(College of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China)Chun Hong XIE (Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China) |
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Abstract: | This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate and singular semilinear parabolic equation ut - (xαux)x = ∫0af(u)dx in (0, a)×(0, T) with homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. It is also proved that the blow-up set is the whole domain, which differs from the local case. Furthermore, the blow-up rate is precisely determined for that in the special cases: f(u) = up, p > 1 and f(u) = eu. |
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Keywords: | Degenerate and singular parabolic equations Nonlocal source Global existence |
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