TY - JOUR
T1 - Lack of BV bounds for approximate solutions to the p-system with large data
AU - Bressan, Alberto
AU - Chen, Geng
AU - Zhang, Qingtian
PY - 2014/4/15
Y1 - 2014/4/15
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2014.01.032
DO - 10.1016/j.jde.2014.01.032
M3 - Article
AN - SCOPUS:84893778400
SN - 0022-0396
VL - 256
SP - 3067
EP - 3085
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -