On Reducibility of Beam Equation with Quasi-periodic Forcing Potential  

作　　者：CHANG JING Li Yong 

机构地区：[1]College of Information Technology,Jilin Agricultural University,Changchun,130118 [2]School of Mathematics,Jilin University,Changchun,130012 [3]不详

出　　处：《Communications in Mathematical Research》2016年第4期289-302,共14页数学研究通讯（英文版）

基　　金：The Science Research Plan(Jijiaokehezi[2016]166)of Jilin Province Education Department During the 13th Five-Year Period;the Science Research Starting Foundation(2015023)of Jilin Agricultural University

摘　　要：In this paper, the Dirichlet boundary value problems of the nonlinear beam equation utt ＋ △^2u ＋ αu ＋ εφ（t）（u ＋ u^3） = 0 , α 〉 0 in the dimension one is considered, where u（t,x） and φ（t） are analytic quasi-periodic functions in t, and e is a small positive real-number parameter. It is proved that the above equation admits a small-amplitude quasi-periodic solution. The proof is based on an infinite dimensional KAM iteration procedure.In this paper, the Dirichlet boundary value problems of the nonlinear beam equation utt ＋ △^2u ＋ αu ＋ εφ（t）（u ＋ u^3） = 0 , α 〉 0 in the dimension one is considered, where u（t,x） and φ（t） are analytic quasi-periodic functions in t, and e is a small positive real-number parameter. It is proved that the above equation admits a small-amplitude quasi-periodic solution. The proof is based on an infinite dimensional KAM iteration procedure.

关 键 词：beam equation infinite dimension Hamiltonian system KAM theory REDUCIBILITY 

分 类 号：O175[理学—数学]