| 一类聚合方程Cauchy问题解的存在唯一性 |
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| 引用本文： | 边东芬,胡越.一类聚合方程Cauchy问题解的存在唯一性[J].江汉大学学报(自然科学版),2010,38(4):5-8. |
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| 作者姓名： | 边东芬 胡越 |
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| 作者单位： | 河南理工大学数学与信息科学学院; |
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| 基金项目： | 河南省高校科技创新人才计划项目，河南省杰出青年科学基金 |
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| 摘 要： | 在Δk∈Lp(Rn),u0∈Lp(Rn)或u0 ∈Lp(Rn)n∩Lp(Rn),其中p,p'∈1,+∞]满足p/1+p/1'=1条件下,证明了耗散型聚合方程Cauchy问题是局部适定的.进一步地,在Δk ∈L∞(Rn),初值u0≥0满足u0 ∈L(R*)条件下,证明了耗散型聚合方程Cauchy问题是整体适定的.
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| 关 键 词： | 耗散型聚合方程 适定性 Banach压缩映射原理 |
Existence and Uniqueness of Solutions to the Cauchy Problem for a Class of Aggregation Equations |
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| BIAN Dong-fen,HU Yue.Existence and Uniqueness of Solutions to the Cauchy Problem for a Class of Aggregation Equations[J].Journal of Jianghan University:Natural Sciences,2010,38(4):5-8. |
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| Authors: | BIAN Dong-fen HU Yue |
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| Institution: | BIAN Dong-fen,HU Yue(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454000,Henan,China) |
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| Abstract: | On the condition that Δk Lp n,and u0 Lp＇ n or u0 L1 n ∩Lp＇ n,wherep,p＇ 1,＋ satisfy p1 ＋ p1＇ = 1,the local well-posedness of the Cauchy problem for diffusiveaggregation equations is obtained.Furthermore,on the condition that Δk L n and the initial data u0 0 satisfies u0 L1 n,the global well-posedness of the Cauchy problem for diffusive ag-gregation equations is proved. |
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| Keywords: | diffusive aggregation equation well-posedness Banach contraction principle |
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