Instability in a reaction - diffusion system with open constant flow may be absolute or convective. In this paper we study these instabilities in the case when the flow decelerates in space. As а model system we consider the one-dimensional Brusselator with flow in the conical reactor. Due to decreasing of the flow rate along the spatial coordinate, the instability is convective near the reactor inlet and absolute at the downstream end. In the sustained regime the instabilities are separated by the stationary wave front. Provided in the paper numerical investigation shows that the front is located near the critical rate point, the point where the flow rate corresponds to transition from convective to absolute instability in the respective spatially uniform system.