一类非线性复Boussinesq方程的初边值问题

The Initial Boundary Value Problem for a Class of Complex Semilinear Boussinesq Equations

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.

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(u^2)_(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)=ε~2(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.