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On the competitive growth of two sand heaps

A simple quasistationary model for the growth of 1D sand heaps in form of a non‐linear system of ordinary differential equations is presented. The basic assumption for the model is the instantaneous deposition of the matter which is poured by punctiform sources. Existence and uniqueness of the solution is shown, and the qualitative evolution, especially the overrun phenomenon, is described. Copyright © 2003 John Wiley & Sons, Ltd.