On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation
Zhang, Ping ; Zheng, Yuxi
Journées équations aux dérivées partielles, (2004), p. 1-12 / Harvested from Numdam
@article{JEDP_2004____A12_0,
     author = {Zhang, Ping and Zheng, Yuxi},
     title = {On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2004},
     pages = {1-12},
     doi = {10.5802/jedp.12},
     zbl = {1068.35074},
     mrnumber = {2135607},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2004____A12_0}
}
Zhang, Ping; Zheng, Yuxi. On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation. Journées équations aux dérivées partielles,  (2004), pp. 1-12. doi : 10.5802/jedp.12. http://gdmltest.u-ga.fr/item/JEDP_2004____A12_0/

[1] R. J. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98(1989), pp. 511–547. | MR 1022305 | Zbl 0696.34049

[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 877643 | Zbl 0626.35059

[3] P. Gerard, Microlocal defect measures, Comm. in Partial Differential Equations, 16 (1991), pp. 1761–1794. | MR 1135919 | Zbl 0770.35001

[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 1400796 | Zbl 0879.35107

[5] J. K. Hunter and R. A. Saxton, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498–1521. | MR 1135995 | Zbl 0761.35063

[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 0834.35085

[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 1297533 | Zbl 0857.35087

[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 1637634 | Zbl 0908.76004

[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 1069518 | Zbl 0774.35008

[10] Ping Zhang and Yuxi Zheng, Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations, 26 (2001), pp. 381-420. | MR 1842038 | Zbl 0989.35112

[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 1799274 | Zbl 0982.35062

[12] Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation, Arch. Rat. Mech. Anal., 166 (2003), pp. 303-319. | MR 1961443 | Zbl 1029.35173

[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 2124163 | Zbl 1082.35129