dc.contributor.author 倪志仁 dc.date.accessioned 2017-11-14T02:50:39Z dc.date.available 2017-11-14T02:50:39Z dc.date.issued 2006-07-30 dc.identifier.citation 厦门大学学报(自然科学版),2006,(04):16-19 dc.identifier.issn 0438-0479 dc.identifier.other XDZK200604002 dc.identifier.uri https://dspace.xmu.edu.cn/handle/2288/154696 dc.description.abstract 对于非Newton多方渗流方程ut=div(|um|p-2 um),(m≥1,p≥2)Cauchy问题解的惟一性,本文在给出了一般意义上的弱解定义之后,在假设初值满足0≤u0(x)∈L1(Rn)∩L∞(Rn)的条件下,得到了一个新的结果.在证明中首先应用了Steklov均值方法得到一个关键恒等式,其次应用partial summation技巧和处理关于空间和时间双变量的Kruzhkov方法论证了一个比较定理,最后证明了Cauchy问题弱解的惟一性. dc.description.abstract The Cauchy problem for the non-newton polypropic filtration equation u_t=div(|u~m|~(p-2)u~m) is considered in this paper,where m≥1,p≥2.After giving the definition of the weak solution of the equation above,and assuming that 0≤u_0(x)∈L~1(R~n)∩L~∞(R~n) a new result about the uniqueness of weak solutions of this equation is obtained.The main tools used in the proofs are Steklov mean value method,partial summation skill and Kruzhkov′s method of doubling variables both in space and time.A comparison principle is obtained and the uniqueness of weak solutions of the Cauchy problem is proved. dc.language.iso zh_CN dc.subject 非Newton多方渗流方程 dc.subject 弱解 dc.subject Cauchy问题 dc.subject polypropic filtration equations dc.subject weak solution dc.subject Cauchy problem dc.title 非Newton多方渗流方程Cauchy问题弱解的惟一性 dc.title.alternative Uniqueness of Weak Solutions of the Cauchy Problem for a Non-Newton Polypropic Filtration Equations dc.type Article
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