IJPAM: Volume 61, No. 4 (2010)

APPROXIMATION AS ATTEMPT TO INFER NONEXISTENCE
OF WEAK SOLUTIONS OF RIEMANN PROBLEMS FOR
THE ``TWO-DIMENSIONAL P-SYSTEM"

Michael Sever
Department of Mathematics
The Hebrew University
Givat Ram, Jerusalem, 91904, ISRAEL
e-mail: sever@math.huji.ac.il


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
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 4