| 一类快扩散方程解的消失及衰减估计 |
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| 引用本文： | 方钟波,李刚.一类快扩散方程解的消失及衰减估计[J].中国海洋大学学报(自然科学版),2011,41(10):128-130. |
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| 作者姓名： | 方钟波 李刚 |
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| 作者单位： | 中国海洋大学数学科学学院,山东青岛,266100 |
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| 基金项目： | 国家留学回国人员科研启动基金项目(910937020)资助 |
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| 摘 要： | 利用积分模估计的方法研究一维与二维情形中快扩散方程解的消失现象。研究过程中巧妙利用低维空间中的Sobolev嵌入不等式和Hlder不等式得出解发生消失的充分条件及其衰退估计。特别是,临界情形时解的消失行为依赖于拉普拉斯算子的第一特征值。
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| 关 键 词： | 快扩散方程 消失 衰减估计 |
Extinction and Decay Estimate of the Solutions for a Class of Fast Diffusion Equations |
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| FANG Zhong-Bo,LI Gang.Extinction and Decay Estimate of the Solutions for a Class of Fast Diffusion Equations[J].Periodical of Ocean University of China,2011,41(10):128-130. |
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| Authors: | FANG Zhong-Bo LI Gang |
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| Institution: | FANG Zhong-Bo,LI Gang(School of Mathematical Science,Ocean University of China,Qingdao 266100,China) |
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| Abstract: | In this paper,we investigate extinction of solutions for the fast diffusion equations by using integral norm estimate method,and we use Sobolev imbedding inequality and H lder's inequality to find the sufficient condition for the existence of extinction solution and its decay estimates.In particular,the extinction behaviour of solutions depend on the first eigenvalues of Laplacian operator in the critical case. |
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| Keywords: | fast diffusion equation extinction decay estimate |
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