Static Solutions of Mixed Burgers-KdV Equation II (Journal of Partial Differential Equations, 1990)
Based on the method of qualitative research in ordinary differential equations, lt is proved that, for any given positive &#946 and &#978, and for any given real a, b and c, the Burgers-KdV equation u_t + uu_x - &#978u_{xx} + &#946u_{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.