Abstract
In this paper, we consider the interaction problem of two centered rarefaction waves for the one-dimensional granular flow equations, which originates from the interaction and impact of two avalanche flows, mud flows or tsunamis in reality. This interaction problem is essentially a Goursat-type boundary value problem in mathematical theory. When there is no vacuum in the initial data, we show that no vacuum appears in the interaction region, while the vacuum occurs when the collision time is sufficiently large. Based on the characteristic method, the a priori estimates are derived to establish the existence and uniqueness of smooth solutions for the Goursat problem on the whole interaction region.
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