Analyticity and Smoothing Effect for the Coupled System of Equations of Korteweg-de Vries Type with a Single Point Singularity

被引：3

作者：

Alves, Margareth S. ^{[3
]}

Calsavara, Bianca M. R. ^{[4
]}

Munoz Rivera, Jaime E. ^{[5
]}

Sepulveda, Mauricio ^{[1
,2
]}

Vera Villagran, Octavio ^{[6
]}

机构：

[1] Univ Concepcion, CI2MA, Concepcion, Chile

[2] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile

[3] Univ Fed Vicosa, Dept Matemat, BR-36570000 Vicosa, MG, Brazil

[4] Univ Estadual Campinas, UNICAMP, Limeira, SP, Brazil

[5] Natl Lab Sci Computat, BR-25651070 Rio De Janeiro, Brazil

[6] Univ Bio Bio, Dept Matemat, Concepcion, Chile

来源：

ACTA APPLICANDAE MATHEMATICAE | 2011年 / 113卷 / 01期

关键词：

Evolution equations; Bourgain space; Smoothing effect;

D O I：

10.1007/s10440-010-9586-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using Bourgain spaces and the generator of dilation P=3t a, (t) +x a, (x) , which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0.

引用

页码：75 / 100

页数：26

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