Global Stability of Traveling Fronts and Convergence Towards Stacked Families of Waves in Monotone Parabolic Systems

Source abstract

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