一类聚合方程Cauchy问题解的存在唯一性  

Existence and Uniqueness of Solutions to the Cauchy Problem for a Class of Aggregation Equations

作　　者：边东芬[1] 胡越[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《江汉大学学报（自然科学版）》2010年第4期5-8,共4页Journal of Jianghan University：Natural Science Edition

基　　金：河南省高校科技创新人才计划(2009HASTIT007);河南省杰出青年科学基金(104100510015)

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.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.

关 键 词：耗散型聚合方程 适定性 BANACH压缩映射原理 

分 类 号：O175.22[理学—数学]