一类广义BBM型方程的整体强解

The Global Strong Solutions For The Generalized BBM Equations

本文考虑广义BBM型方程u_1-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。

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.