A SHARP CONDITION FOR THE WELL-POSEDNESS OF THE LINEAR KDV-TYPE EQUATION

被引：9

作者：

Akhunov, Timur ^{[1
]}

机构：

[1] Univ Calgary, Dept Math, Calgary, AB T2N 1N4, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 142卷 / 12期

关键词：

KdV; linear; dispersive; partial differential equations; energy method; Mizohata condition; CAUCHY-PROBLEM; DISPERSIVE EQUATIONS; REGULARITY;

D O I：

10.1090/S0002-9939-2014-12136-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An initial value problem for a very general linear equation of KdV-type is considered. Assuming non-degeneracy of the third derivative coefficient, this problem is shown to be well-posed under a certain simple condition, which is an adaptation of the Mizohata-type condition from the Schrodinger equation to the context of KdV. When this condition is violated, ill-posedness is shown by an explicit construction. These results justify formal heuristics associated with dispersive problems and have applications to non-linear problems of KdV-type.

引用

页码：4207 / 4220

页数：14

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