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We derive exact solutions of one-dimensional Euler system that accounts for gravity together with large friction. Certain optimal classes of subalgebra using Lie symmetry analysis are obtained for this system. We apply the reduction procedure to reduce the Euler system to a system of ordinary differential equations in terms of new similarity variable for each class of subalgebras leading to invariant solutions. The evolution of characteristic shock and its interaction with the weak discontinuity by using one of the invariant solutions is studied. Further, the properties of reflected and transmitted waves and jump in acceleration influenced by the incident wave have been characterized. KEYWORDS euler system with large friction, invariant solution, lie symmetry analysis, optimal classification, wave interactions, weak discontinuity MSC CLASSIFICATION 35A30; 35C05; 35L60; 35Q35; 76D33 Math Meth Appl Sci. 2020;43:5744-5757. wileyonlinelibrary.com/journal/mma

In this article, we discuss the wave interactions in pressureless Cargo-LeRoux model with flux perturbation. The corresponding Riemann solution in terms of a one-parameter family of curves is presented. We prove the existence and uniqueness of the solution to the Riemann problem and construct estimates for the components of the solution. Relevant amplitudes are determined while presenting the interactions of weak discontinuity with contact discontinuity and shock waves. Further, we discuss the interaction of weak shocks in detail. Finally, some test cases are treated to understand the effect of initial data and strength of the shock on the transmitted, reflected amplitudes, and jump in the acceleration of the shock.