【摘要】 研究了一类非线性复Boussinesq方程的初边值问题:utt-auttxx-ibuttx-2dutxx=-αuxxxx+uxx+β(u2)xx,　x∈(0,π),t>0,u(0,t)=u(π,t)=0,t>0,uxx(0,t)=uxx(π,t)=0,t>0,u(x,0)=ε2(x),ut(x,0)=ε2ψ(x),x∈(0,π).以复值富里埃级数的形式得出了该方程的整体解的适定性.更多还原

【Abstract】 This paper deals with the initial boundary value problem for the following damped Boussinesq equation:u_tt-au_ttxx-ibu_ttx-2du_txx=-αu_xxxx+u_xx+β（u²）_xx, x∈（0,π）,t>0, u（0,t）=u（π,t）=0,t>0, u_xx（0,t）=u_xx（π,t）=0,t>0, u（x,0）=ε²（x）,u_t（x,0）=ε²ψ（x）,x∈（0,π）.A global solution of the equation in the form of Fouries series is derived.更多还原