IJPAM: Volume 61, No. 4 (2010)
OF WEAK SOLUTIONS OF RIEMANN PROBLEMS FOR
THE ``TWO-DIMENSIONAL P-SYSTEM"
Department of Mathematics
The Hebrew University
Givat Ram, Jerusalem, 91904, ISRAEL
e-mail: [email protected]
Abstract.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.
Received: May 1, 2010
AMS Subject Classification: 35L65
Key Words and Phrases: multidimensional conservation laws, self-similar solutions, approximation methods
Source: International Journal of Pure and Applied Mathematics