| Properties of positive solutions to a nonlinear parabolic problem |
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| 作者姓名： | Hui-ling LI & Ming-xin WANG |
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| 作者单位： | Hui-ling LI & Ming-xin WANG Department of Mathematics，Southeast University，Nanjing 210018，China |
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| 基金项目： | 国家自然科学基金;教育部重点工程基金 |
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| 摘 要： | This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.
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| 收稿时间： | 12 October 2005 |
| 修稿时间： | 22 November 2006 |
Properties of positive solutions to a nonlinear parabolic problem |
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| Hui-ling LI & Ming-xin WANG.Properties of positive solutions to a nonlinear parabolic problem[J].Science in China(Mathematics),2007,50(4):590-608. |
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| Authors: | Hui-ling Li Ming-xin Wang |
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| Institution: | Department of Mathematics,Southeast University,Nanjing 210018,China |
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| Abstract: | This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption
and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms
of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vázquez and the comparison principle,
we deduce that the blow-up occurs only on the boundary ∂Ω. In addition, for a bounded Lipschitz domain Ω, we establish the
blow-up rate estimates for the positive solution to this problem with a = 0.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471022 and 10601011) and Key Project
of the Ministry of Education of China (Grant No. 104090) |
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| Keywords: | quasilinear parabolic equation blow-up global existence blow-up rate blow-up set |
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