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
N1 - Funding Information:
The research of the first author was partially supported by NSF, with grant DMS-1411786: “Hyperbolic Conservation Laws and Applications”. The fourth author is supported in part by National Natural Science Foundation of China under grant 11231006, Natural Science Foundation of Shanghai under grant 14ZR1423100 and China Scholarship Council.
Publisher Copyright:
© 2015 World Scientific Publishing Company.
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.
UR - http://www.scopus.com/inward/record.url?scp=84954516523&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954516523&partnerID=8YFLogxK
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 -