化粪池图集.ppt

黑龙江大学硕士学位论文关键词: 带阻尼的半线性波动方程;有限差分方法;L矽印伽l铡泛函;梯度动力系统;整体吸引子; 一Ⅱ一 Abstract Abstract Infinitedimensional dynamical system is an important branch ofdynamical sys- terns,which iswidely used inmany areas,and gradually e the main study object andsubjects ofthedynamical thestudy,where theglobal attrac- tor determines the finalstate ofthe infinite-dimensional dynamical systems,and reflecting the long time behavior ofinfinitedimensional dynamical the rapid development puter,numerical simulation puters of inthe infinite-dimensional dynamical system has e surprisingly mature:the finite difference method is anumerical method based on thediscrete equations and solving region,it makes acontinuous infinitedimensional dynamical system tobediscrete,SO that itCan benumerical approximated puters,and which is one monly used thispaper,we consider theproblem ofthe long time behavior oftheone-dimensional Damped semilinear wave equations whit themeaals offinitedifference methods. Here gives thesemilineardamped wave equation 铲钍况2+2Q甓一△u=州牡)-9(吐 where(x,t)∈Q×(0,+∞),andQ=[0, theboundary condition and the initialcondition iS u(0)=u(L)=0, 厂au、 L%瓦夕 t=O (咖,妒), Inthispaper,the firstchapter outlines the development history and current situ- ation ofinfinitedimensional dynamical system,as well as the application offinite difference method tosolve the problem ofdynamical syst