廣義可壓縮彈性桿方程解的爆破條件

姜玲玉

(中央財經大學應用數學學院,北京 100081)

廣義可壓縮彈性桿方程解的爆破條件

姜玲玉

(中央財經大學應用數學學院,北京 100081)

研究廣義可壓縮彈性桿方程解的爆破條件及尖峰孤立波解的存在性.首先利用所建立的爆破準則,給出一個方程在有限時刻爆破的充分條件.其次,嚴格證明了其尖峰孤立波解的整體存在性.該結果豐富了此類Camassa-Holm型方程的研究.

廣義可壓彈性桿波動方程;爆破;尖峰孤立波解

DO I：10.3969/j.issn.1008-5513.2013.05.003

1 引言

2 解的爆破

3 尖峰孤立波解的存在性

參考文獻

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W ave-b reaking phenom ena for a generalized com p ressib le elastic-rod equation

Jiang Lingyu

(Department of M athematics,Central University of Finance and Econom ics,Beijing 100081,China)

We investigate in the paper the wave-breaking phenomenon of a generalized hyperelastic-rod wave equation,which occurs in f nite time for certain initialp rof les.M oreover,we obtain the existence of some peaked solitary wave solu tions.The results obtained enriches the research of the type of the Cam assa-Holm equation.

generalized hyperelastic-rod wave equation,b low-up phenom enon,peaked solitary wave solutions

O175.29

A

1008-5513(2013)05-0458-07

2008-02-10.

國家自然科學基金(11171241).

姜玲玉(1969-),副教授,研究方向：非線性偏微分方程.

2010 MSC:35J15