Abstract
In this paper a p-system with relaxation is considered. Within the theoretical framework of the differential constraints method, we determine two possible classes of exact solutions of the governing model both parameterized by one arbitrary function. This allows to solve classes of initial value problems of interest in nonlinear wave propagation. In fact a generalized Riemann problem is solved by determining a smooth solution which plays the role of the well known rarefaction wave of the homogeneous case.
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