Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

► An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. ► The density ahead of the shock is taken as a power of the position from the origin of the shock wave. ► For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. ► The solution obtained for the planer, and cylindrically symmetric flow is new one. ► The results obtained are also presented graphically for different Mach numbers.