Global Existence of Solutions of an Extended Landau Equation

The existence of solutions of a certain integro-differential equation, which contains a small parameter, is studied. This equation describes the amplitude of a disturbance of a boundary layer as a function of time. The present paper deals with the case of a weakly unstable boundary-layer flow. In this case, the amplitude equation is shown to have solutions, which are defined for all times, if the parameter of the equation is chosen sufficiently small. These solutions are determined uniquely by their initial values and tend to a common limit as time goes to infinity.