Long time behaviour of the solution of a system of equations from new theory of shock dynamics

AbstractThe new theory of shock dynamics gives a system of n + 2 equations, the solution of which determines the propagation of a discontinuity in the initial condition. For the model equation ut + u ux = 0, the long time behaviour of the solution is investigated for various confined initial data. The suitability of using Padé approximants for the solution is examined. Special exact solutions are obtained