Weak asymptotic solution of one dimensional zero pressure dynamics system in the quarter plane

In this paper we study a system of equations which appear in the modelling of many physical phenomena. Initially this system appeared in description of the large scale structure formation. Recently it is derived as a second order queueing model. We construct weakly asymptotic solutions of the initial boundary value problem for the system and interaction of waves in the quarter plane {(x,t):x>0,t>0}$\lbrace (x,t): x>0,t>0\rbrace$ with boundary Riemann solution centered at (0,0) and Riemann solution centered at a point (x0,0),x0>0$(x_0,0), x_0>0$.