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Preprint 2013-010

Lack of BV bounds for approximate solutions to the p-system with large data

Alberto Bressan, Geng Chen, and Qingtian Zhang

Abstract: We consider front tracking approximate solutions to the p-system of isentropic gas dynamics. At interaction times, the outgoing wave fronts have the same strength as in the exact solution of the Riemann problem, but some error is allowed in their speed. For large BV initial data, we construct examples showing that the total variation of these approximate solutions can become arbitrarily large, or even blow up in finite time. This happens even if the density of the gas remains uniformly positive.

Paper:
Available as PDF (327 Kbytes).
Author(s):
Alberto Bressan,
Geng Chen,
Qingtian Zhang,
Submitted by:
; 2013-10-25.