Computability of solutions of the Korteweg-de Vries equation

被引：0
|
作者：
Gay, W
Zhang, BY
Zhong, N
机构：
[1] Univ Cincinnati, Clermont Coll, Batavia, OH 45103 USA
[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA
来源：
MATHEMATICAL LOGIC QUARTERLY | 2001年 / 47卷 / 01期
关键词：
initial value problem; KdV equation; Sobolev space;
D O I：
10.1002/1521-3870(200101)47:1<93::AID-MALQ93>3.0.CO;2-C
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study computability of the solutions of the Korteweg-de Vries (KdV) equation u(t) + uu(x) + u(xxx) = 0. This is one of the open problems posted by Pour-El and Richards [25]. Based on Bourgain's new approach to the initial value problem for the KdV equation in the periodic case, we show that the periodic solution u(x, t) of the KdV equation is computable if the initial data is computable.
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页码：93 / 110
页数：18
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