On a heat conduction problem by Myshkis

被引：7

作者：

Chen, YMJ

Chow, YS ^{[1
]}

Hsieh, J

机构：

[1] Acad Sinica, Inst Math, Taipei 11529, Taiwan

[2] Tamkang Univ, Dept Math, Tamsui 25137, Taipei, Taiwan

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2000年 / 6卷 / 03期

关键词：

difference equation; heat equation; asymptotic behavior; recurrent relation;

D O I：

10.1080/10236190008808230

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let tau(1) = 1, tau(2), tau(3), ... be recurrently defined by Sigma(j=1)(n)(Sigma(s=j)(n)tau s)(-1/2) = 1 for n = 2, 3, ... The sequence {tau(n)} appeared in a heat conduction problem studied by Myshkis (J. Differ. Equations Appl. 3, 1997, 89-91), He proposed as an open problem the asymptotic expression for tau(n). It is shown in this paper that tau(n) is increasing and lim(n) tau(n)/n = pi(2)/2. AMS Subject Classification: 39A10, 35K05, 93B52.

引用

页码：309 / 318

页数：10

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