ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A HIGHER-ORDER KDV-TYPE EQUATION WITH CRITICAL NONLINEARITY

被引：3

作者：

Okamoto, Mamoru ^{[1
]}

机构：

[1] Shinshu Univ, Div Math & Phys, Fac Engn, 4-17-1 Wakasato, Nagano 3808553, Japan

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2019年 / 8卷 / 03期

关键词：

Higher-order KdV-type equation; asymptotic behavior; critical non-linearity; self-similar solution; LONG-TIME BEHAVIOR; SCHRODINGER-EQUATION; WELL-POSEDNESS; SCATTERING; STABILITY; EXISTENCE; SPACE; MKDV;

D O I：

10.3934/eect.2019027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem of the higher-order KdV-type equation: partial derivative(t)u + 1/m vertical bar partial derivative(x)vertical bar(m-1)partial derivative(x)u = partial derivative(x)(u(m)) where m >= 4. The nonlinearity is critical in the sense of long-time behavior. Using the method of testing by wave packets, we prove that there exists a unique global solution of the Cauchy problem satisfying the same time decay estimate as that of linear solutions. Moreover, we divide the long-time behavior of the solution into three distinct regions.

引用

页码：567 / 601

页数：35

共 28 条

[1] A STEEPEST DESCENT METHOD FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS - ASYMPTOTICS FOR THE MKDV EQUATION [J].