Exact solutions of Euler equations of ideal gasdynamics via Lie group analysis (Q971873)

Using results from [\textit{A. Donato} and \textit{T. Ruggeri}, J. Math. Anal. Appl. 251, 395--405 (2000; Zbl 0991.76072)], the authors explicitly characterize a class of solutions to the first order quasilinear system of partial differential equations (PDEs) governing one dimensional unsteady planar and radially symmetric flows of an adiabatic gas involving shock waves. Since the system involves only two independent variables, two commuting Lie vector fields are needed, which are constructed by taking a linear combination of the infinitesimal operators of the Lie point symmetries admitted by the system at hand. With the help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous system, whose simple solutions provide nontrivial solutions of the original system.