【摘要】 本文考虑广义BBM型方程u₁-u_xxt+f（u）_x=g（x,t）-h（u）+σ（u_x）x的初边值问题、周期边界问题和初值问题。假设f,g,h,σ及初值满足一定条件下,证明了上述各类问题整体强解的存在唯一性;进一步,f,g,h,σ及初值满足一定光滑性条件下,得到了整体强解的光滑性。更多还原

【Abstract】 In this paper we consider the initial-boundary value problem, the periodic problem and the initial value problem for the generalized BBM equation u_t-u_xxt+f（u）_x=g（x,t）+h（u）+σ（u_x）_x. Suppose that f, g, h, σ satisfy some conditions, we obtain the existence and uniqueness of the global strong solution; Further more, if, g, h, σ satisfy some smooth conditions, we obtain the smoothness of the strong solutions.更多还原