| ZERO-DIMENSIONAL GLOBAL ATTRACTOR OF DAMPED SINE-GORDON EQUATION |
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| 作者姓名： | 秦文新 周盛凡 |
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| 作者单位： | QIN WENXIN (Department of Mathematics，Suzhou University，Suzhou 215006，China)ZHOU SHENGruN(Department of Mathematics，Sichuan University，Chengdu 610064，China) |
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| 摘 要： | 1.IntroductionandMainResultsInthispaper,weconsiderthedampedsine-Gordonequation,withhomogeneousDirichletboundarycondition:whereu=u(x,t)ER,xEn,fiisaboundeddomaininRe(m=1,2,3)withsmoothboundaryoff,thedampingcoefficientor>0,thediffusingconstantd>0.Inthesequel,insteadofconsideringsystem(1.1),weinvestigatethefollowingsysteminHilbertspaceE=Ha(fi)xL'(fl):inwhichu(t)CHI(fl),v(t)6L'(fl)foranyt>0,A=--dA,G(u)=(--sine f),fEHa(~~),noEV.=Ha(~~),itoEH.=L'(fl).Let11'Onlayrwriteequatioll(l.2)asillwhi…
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| 收稿时间： | 30 December 1994 |
Zero-dimensional global attractor of damped sine-gordon equation |
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| Qin Wenxin,Zhou Shengfan.ZERO-DIMENSIONAL GLOBAL ATTRACTOR OF DAMPED SINE-GORDON EQUATION[J].Acta Mathematicae Applicatae Sinica,1998,14(3):260-264. |
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| Authors: | Qin Wenxin Zhou Shengfan |
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| Institution: | (1) Department of Mathematics, Suzhou University, 215006 Suzhou, China;(2) Department of Mathematics, Sichuan University, 610064 Chengdu, China |
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| Abstract: | We investigate the global attractor of damped sine-Gordon equation with homogeneousDirichlet boundary condition. We prove the existence of global attractor. Under some conditionson the parameters, we show the global attractor is zero-dimensional and is exactly the uniqueequilibrium point of the system. |
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| Keywords: | Global attractor sine-Gordon equation equilibrium point Lyapunov function |
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