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.
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页码：567 / 601
页数：35
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