【摘要】 研究如下方程utt -aiuttx - 2butxx =-cuxxxx +uxx +β(u2 ) xx,u(0 ,t) =u(π ,t) =0 ,　t>0 ,uxx(0 ,t) =uxx(π ,t) =0 ,　t>0 ,u(x ,0 ) =ε2 φ(x) ,ut(x ,0 ) =ε2 ψ(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 following damped Boussinesq equationu tt -a i u ttx -2bu txx =-cu xxxx +u xx +β(u 2) xx ,u(0,t)=u( π ,t)=0, t>0, u xx (0,t)=u xx ( π ,t)=0, t>0, u(x,0)=ε 2φ(x),u t(x,0)=ε 2ψ(x), x∈(0, π ).A global solution of the equation in the form of Fouries series is derived.更多还原