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《Journal of Shaanxi University of Technology(Natural Science Edition)》 2012-06
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On the stability of equilibrium point of the second order partial differential equation with quasiperiodic coefficients

CHENG Xiao-jing,HONG Jie(Scholl of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723000,China)  
This paper gives a simple and feasible method of judging the stability of partial differential equations about equilibrium points.That is for the equation ut-uxx+c(t)u=0 and u(t,0)=u(t,2π)=0,where u(t,x)=Σ+∞ n=1qn(t)φn(x),φn(x) is a eigenfunction to eigenvalue λ in y″=-λy and y(0)=y(2π)=0,c(t)=α+εc1(t),α is a positive constant,c1(t) is sufficient smooth quasiperiodic function with frequencies ω.Combining the theory KAM,it proves that the equation is reducible for most of sufficient small,and finally the result of using about the stability of the equilibrium is given.
【Fund】: 陕西理工学院科研基金资助项目(SLGQD0724)
【CateGory Index】: O175.21
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