Abstract
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
| Original language | English (US) |
|---|---|
| Article number | 0252-9599(2001)02-0159-12 |
| Pages (from-to) | 159-170 |
| Number of pages | 12 |
| Journal | Chinese Annals of Mathematics. Series B |
| Volume | 22 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 2001 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
Cite this
}
Singular and rarefactive solutions to a nonlinear variational wave equation. / Zhang, Ping; Zheng, Yuxi.
In: Chinese Annals of Mathematics. Series B, Vol. 22, No. 2, 0252-9599(2001)02-0159-12, 01.01.2001, p. 159-170.Research output: Contribution to journal › Article
TY - JOUR
T1 - Singular and rarefactive solutions to a nonlinear variational wave equation
AU - Zhang, Ping
AU - Zheng, Yuxi
PY - 2001/1/1
Y1 - 2001/1/1
N2 - Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
AB - Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
UR - http://www.scopus.com/inward/record.url?scp=0037832701&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037832701&partnerID=8YFLogxK
U2 - 10.1142/S0252959901000152
DO - 10.1142/S0252959901000152
M3 - Article
AN - SCOPUS:0037832701
VL - 22
SP - 159
EP - 170
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
SN - 0252-9599
IS - 2
M1 - 0252-9599(2001)02-0159-12
ER -