Static Solutions of Mixed Burgers-KdV Equation II

Abstract

Based on the method of qualitative research in ordinary differential equations, lt is proved that, for any given positive β and ϒ, and for any given real a, b and c, the Burgers-KdV equation u_t + uu_x - ϒu_{xx} + βu_{xxx} = 0 has at least one, but at most finite Static solutions satisfying the same boundary conditions u(0, t) = a,u(1, t) = b \quad and u_x(1, t) = c on the interval [0, 1] of x. Some sufficient conditions on the global stability for certain statle solutions are given.