GLOBAL STABILITY OF TRAVELING FRONTS AND CONVERGENCE TOWARDS STACKED FAMILIES OF WAVES IN MONOTONE PARABOLIC-SYSTEMS

A class of parabolic systems for which the maximum principle is valid is investigated. When two stable rest points can be connected by a tra veling front, any solution of the Cauchy problem which initially has t hese two rest points as spatial limits will become monotone in finite time on every compact interval and converge to a traveling front. As a n application, convergence to stacked waves is discussed.