Abstract
The aim of this paper is to present two different approaches, both based on Lie symmetry analysis, allowing to obtain solutions of the Riemann problem with non-classical discontinuous initial data for a system of balance laws. The first method uses the invariance with respect to a Lie group of exact point symmetries, whereas the second one is based on the approximate Lie symmetries. The two methods are applied to a particular 2 × 2 system of balance laws describing rate-type materials. Moreover, some numerical simulations are performed in order to validate the approximate solutions and check that the exact solution, as a parameter involved in the initial conditions tends to zero, approaches the solution of the classical Riemann problem.
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