@incollection{JEDP_2004____A12_0,
author = {Ping Zhang and Yuxi Zheng},
title = {On the {Global} {Existence} of {Weak} {Solutions} to {A} {Nonlinear} {Variational} {Wave} {Equation}},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {12},
pages = {1--12},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2004},
doi = {10.5802/jedp.12},
mrnumber = {2135607},
zbl = {1068.35074},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.12/}
}
TY - JOUR AU - Ping Zhang AU - Yuxi Zheng TI - On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation JO - Journées équations aux dérivées partielles PY - 2004 SP - 1 EP - 12 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.12/ DO - 10.5802/jedp.12 LA - en ID - JEDP_2004____A12_0 ER -
%0 Journal Article %A Ping Zhang %A Yuxi Zheng %T On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation %J Journées équations aux dérivées partielles %D 2004 %P 1-12 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.12/ %R 10.5802/jedp.12 %G en %F JEDP_2004____A12_0
Ping Zhang; Yuxi Zheng. On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation. Journées équations aux dérivées partielles (2004), article no. 12, 12 p. doi : 10.5802/jedp.12. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.12/
[1] R. J. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98(1989), pp. 511–547. | MR | Zbl
[2] R. J. DiPerna and A. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys., 108(1987), pp. 667–689. | MR | Zbl
[3] P. Gerard, Microlocal defect measures, Comm. in Partial Differential Equations, 16 (1991), pp. 1761–1794. | MR | Zbl
[4] R. T. Glassey, J. K. Hunter, and Yuxi Zheng, Singularities in a nonlinear variational wave equation, J. Differential Equations, 129(1996), pp. 49–78. | MR | Zbl
[5] J. K. Hunter and R. A. Saxton, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498–1521. | MR | Zbl
[6] J. K. Hunter and Yuxi Zheng, On a nonlinear hyperbolic variational equation I and II, Arch. Rat. Mech. Anal., 129 (1995), pp. 305-353 and 355-383. | Zbl
[7] J. L. Joly, G. Métivier, and J. Rauch , Focusing at a point and absorption of nonlinear oscillations, Trans. Amer. Math. Soc., 347(1995), pp. 3921–3970. | MR | Zbl
[8] P. L. Lions , Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible Models, Lecture series in mathematics and its applications, V. 6, Clarendon Press , Oxford, 1998. | MR | Zbl
[9] L. Tartar, H-measures, a new approach for studying homogenisation oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburg Sect. A, 115 (1990), pp.193-230. | MR | Zbl
[10] Ping Zhang and Yuxi Zheng, Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations, 26 (2001), pp. 381-420. | MR | Zbl
[11] Ping Zhang and Yuxi Zheng, Existence and uniqueness of solutions to an asymptotic equation of a variational wave equation with general data, Arch. Rat. Mech. Anal., 155 (2000), pp. 49-83. | MR | Zbl
[12] Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation, Arch. Rat. Mech. Anal., 166 (2003), pp. 303-319. | MR | Zbl
[13] Ping Zhang and Yuxi Zheng, Weak Solutions to A Nonlinear Variational Wave Equation with General Data, (to appear Ann. Inst. H. Poincaré Anal. Non Linéaire ). | Numdam | MR | Zbl
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