TY - JOUR
T1 - On finite time BV blow-up for the p-system
AU - Bressan, Alberto
AU - Chen, Geng
AU - Zhang, Qingtian
N1 - Funding Information:
The research of the first author was partially supported by NSF, with grant DMS-1411786: Hyperbolic Conservation Laws and Applications. The research of the second author was partially supported by NSF with grant DMS-1715012.
Publisher Copyright:
© 2018, © 2018 Taylor & Francis.
PY - 2018/8/3
Y1 - 2018/8/3
N2 - The paper studies the possible blowup of the total variation for entropy weak solutions of the p-system, modeling isentropic gas dynamics. It is assumed that the density remains uniformly positive, while the initial data can have arbitrarily large total variation (measured in terms of Riemann invariants). Two main results are proved. (I) If the total variation blows up in finite time, then the solution must contain an infinite number of large shocks in a neighborhood of some point in the t-x plane. (II) Piecewise smooth approximate solutions can be constructed whose total variation blows up in finite time. For these solutions the strength of waves emerging from each interaction is exact, while rarefaction waves satisfy the natural decay estimates stemming from the assumption of genuine nonlinearity.
AB - The paper studies the possible blowup of the total variation for entropy weak solutions of the p-system, modeling isentropic gas dynamics. It is assumed that the density remains uniformly positive, while the initial data can have arbitrarily large total variation (measured in terms of Riemann invariants). Two main results are proved. (I) If the total variation blows up in finite time, then the solution must contain an infinite number of large shocks in a neighborhood of some point in the t-x plane. (II) Piecewise smooth approximate solutions can be constructed whose total variation blows up in finite time. For these solutions the strength of waves emerging from each interaction is exact, while rarefaction waves satisfy the natural decay estimates stemming from the assumption of genuine nonlinearity.
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U2 - 10.1080/03605302.2018.1499115
DO - 10.1080/03605302.2018.1499115
M3 - Article
AN - SCOPUS:85061636612
SN - 0360-5302
VL - 43
SP - 1242
EP - 1280
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 8
ER -