TY - JOUR
T1 - No BV bounds for approximate solutions to p-system with general pressure law
AU - Bressan, Alberto
AU - Chen, Geng
AU - Zhang, Qingtian
AU - Zhu, Shengguo
PY - 2015/12/1
Y1 - 2015/12/1
N2 - For the p-system with large BV initial data, an assumption introduced in [N. S. Bakhvalov, Z. Vycisl. Mat. i Mat. Fiz. (Russian) 10 (1970) 969-980] by Bakhvalov guarantees the global existence of entropy weak solutions with uniformly bounded total variation. The present paper provides a partial converse to this result. Whenever Bakhvalov's condition does not hold, we show that there exist front tracking approximate solutions, with uniformly positive density, whose total variation becomes arbitrarily large. The construction extends the arguments in [A. Bressan, G. Chen and Q. Zhang, J. Diff. Eqs. 256(8) (2014) 3067-3085] to a general class of pressure laws.
AB - For the p-system with large BV initial data, an assumption introduced in [N. S. Bakhvalov, Z. Vycisl. Mat. i Mat. Fiz. (Russian) 10 (1970) 969-980] by Bakhvalov guarantees the global existence of entropy weak solutions with uniformly bounded total variation. The present paper provides a partial converse to this result. Whenever Bakhvalov's condition does not hold, we show that there exist front tracking approximate solutions, with uniformly positive density, whose total variation becomes arbitrarily large. The construction extends the arguments in [A. Bressan, G. Chen and Q. Zhang, J. Diff. Eqs. 256(8) (2014) 3067-3085] to a general class of pressure laws.
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U2 - 10.1142/S0219891615500241
DO - 10.1142/S0219891615500241
M3 - Article
AN - SCOPUS:84954516523
VL - 12
SP - 799
EP - 816
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
SN - 0219-8916
IS - 4
ER -