【摘要】 研究如下带阻尼Boussinesq方程Cauchy问题的整体解utt-auttxx-2butxx=-cuxxxx+uxx-αu+β(up)xx,u(x,0)=ε2(x),　ut(x,0)=ε2ψ(x),其中x∈R1,t>0,a,b,c,α是正常数,β∈R1,ε>0是小参数,p 2是正整数.假设a+c-b2>0时,得到了上面问题整体解的适定性及长时间渐近解.更多还原

【Abstract】 This paper deals with the global solution of the Cauchy problem for the following Boussinesq equationu_tt-au_ttxx-2bu_txx=-cu_xxxx+u_xx-αu+β（u^p）_xx, u（x,0）=ε²（x）,u_t（x,0）=ε²ψ（x）,where x∈R¹,t>0,a,b,c and α are positive constants, β∈R¹,ε is a small positive parameter, p2 is a positive integer. For the case a+c-b²>0, the well-posedness and large time asymptotics of the global solution for the equation are established.更多还原