Abstract: The Cauchy problem for the “bad” Boussinesq-type equation with damping term u_u-u_xx-2ku_xxt-αu_xxxx=β(u<>sup>n)_xx is studied Where k, α and β are real numbers, with k>0,α>0, and n≥2 is an integer It proves that for any T>0 the Cauchy problem admits a global smooth solution u∈C^∞((0,T］;H^∞(R))∩C(［0，T］;H1(R))∩C1(［0，T］;H-1(R)) under suitable assumptions on the initial data

Key words: “bad” Boussinesq-type equation, Cauchy problem, global smooth solution

摘要： 研究一类具阻尼项的“坏”的Boussinesq型方程u_u-u_xx-2ku_xxt-αu_xxxx=β(u<>sup>n)_xx的Cauchy问题，其中k,α为大于零的实数，β是实数，n≥2是整数。在关于初值的适当假设下，证明了Cauchy问题存在一个整体光滑解u∈C^∞((0,T］;H^∞(R))∩C(［0，T］；H1(R))∩C1(［0，T］；H-1(R))对任何T>0。

关键词: “坏”的Boussinesq型方程, Cauchy问题, 整体光滑解