廣義可壓縮彈性桿方程解的爆破條件

姜玲玉

(中央財(cái)經(jīng)大學(xué)應(yīng)用數(shù)學(xué)學(xué)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(cái)經(jīng)大學(xué)應(yīng)用數(shù)學(xué)學(xué)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(zhǔn)則,給出一個(gè)方程在有限時(shí)刻爆破的充分條件.其次,嚴(yán)格證明了其尖峰孤立波解的整體存在性.該結(jié)果豐富了此類Camassa-Holm型方程的研究.

廣義可壓彈性桿波動(dòng)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(xiàn)

[1]Cam assa R,Holm D.An integrable shallow w ater equation w ith peaked solitons[J].Phys.Rev.Letters, 1993,71:1661-1664.

[2]Constantin A,Lannes D.The hydrodynam ical relevance of the Camassa-Holm and Degasperis-Procesi equations[J].A rch.Ration.M ech.Anal.,2009,192:165-186.

[3]Constantin A,Escher J.W ave b reaking for non linear non local shallow water equations[J].Acta M ath., 1998,181:229-243.

[4]Constantin A,Escher J,G lobal existence and b low-up for a shallow water equation[J].Annali Sc.Norm. Sup.Pisa.,1998,26:303-328.

[5]Constan tin A,StraussW A.Stability of a class of solitary waves in com p ressib le elastic rods[J].Phys.Lett. A,2000,270:140-148.

[6]Constantin A,StraussW A.Stability of peakons[J].Comm.Pure App l.M ath.,2000,53:603-610.

[7]X in Z,Zhang P.On the weak solu tions to a shallow water equation[J].Communications on Pure and A pp lied M athematics,2000,53:1411-1433.

[8]羅婷.一類Camassa-Holm型方程的不變子空間及其精確解[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2012,28(5):655-658.

[9]DaiH.M odel equation for non linear dispersivewaves in a com p ressib le M ooney-Rivlin rod[J].Acta M ech., 1998,127:193-203.

[10]DaiH,Huo Y.Solitary shock waves and other travelling waves in a general com p ressible hyperelastic rod[J]. Proc.Roy.Soc.London Ser.A,2000,456:331-363.

[11]Kato T.Quasi-Linear Equations of Evolution,w ith App lications to Partial Dif erential Equations[C]// Spectral Theory and D if erential Equations.Berlin:Sp ringer Verlag,1995.

[12]Gui G,Liu Y,O lver P J,et al.W ave-Breaking and Peakons for a Modifed Camassa-Holm Equation[J]. Comm.Math.Phys.,2013,319:731-759.

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(guó)家自然科學(xué)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