In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t ne... In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ】0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.展开更多
This paper investigated the asymptotic behavior of global weak solutions of the initial boundary value problem for a class of nonlinear wave equations. Moreover, blowup of this kind of equations was also disscussed.
基金the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570, the Open Foundation of State Key Laboratory of High Performance Computing of China, the Research Fund of the National University of Defense Technology under Grant No JC15-02-02, and the Fund from HPCL.
基金supported by National Natural Science Foundation of China (Grant Nos.10531050,10771098)the Major State Basic Research Development of China and the Natural Science Foundation of Jiangsu Province(Grant No.BK2007134)
文摘 In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ】0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.
文摘This paper investigated the asymptotic behavior of global weak solutions of the initial boundary value problem for a class of nonlinear wave equations. Moreover, blowup of this kind of equations was also disscussed.