Reducibility for wave equations of finitely smooth potential with periodic boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Sun, Yingte^1,2  Li, Jing³  Xie, Bing³ 

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Hefei Univ, Dept Math & Phys, Hefei 230601, Anhui, Peoples R China

[3] Shandong Univ, Sch Math & Stat, Weihai 264209, Peoples R China

关键词: KAM theory;    Reducibility;    Quasi-periodic wave operator;    Finitely smooth potential;    Periodic boundary conditions;    Pure-point spectrum;   

DOI  :  10.1016/j.jde.2018.08.044

来源: Elsevier

【 摘 要 】

In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subject to periodic boundary conditions. More exactly, the linear wave equation u(tt) - u(xx) + Mu + epsilon(V-0(omega t)u(xx )+ V(omega t, x)u) = 0, x is an element of R/2 pi Z can be reduced to a linear Hamiltonian system with a constant coefficient operator which is of pure imaginary point spectrum set, where V is finitely smooth in (t, x), quasi-periodic in time t with Diophantine frequency omega is an element of R-n, and V-0 is finitely smooth and quasi-periodic in time t with Diophantine frequency omega is an element of R-n. Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent. (C) 2018 Elsevier Inc. All rights reserved.

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