Approximation as attempt to infer nonexistence of weak solutions of riemann problems for the "Two-dimensional P-System"

A class of Riemann problems for the two-dimensional p-system is considered, for which the existence of a traditional weak solution is at best uncertain. Regarding the existence of such a solution as a postulated hypothesis, we attempt to prove the hypothesis wrong by experiment. In this case, experiment means the construction and analysis of one-parameter sequences of ostensibly approximate solutions, obtained by both vanishing viscosity and discretization methods. In each case, failure of the method to produce a sequence provably converging to the desired solution is shown to be readily observable in the sense of numerical computations. The hypothesis of existence of a solution thus survives to the extent that no such failure is observed.