Zhang, Ping  ; Zheng, Yuxi 1
@article{AIHPC_2005__22_2_207_0,
author = {Zhang, Ping and Zheng, Yuxi},
title = {Weak solutions to a nonlinear variational wave equation with general data},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {207--226},
year = {2005},
publisher = {Elsevier},
volume = {22},
number = {2},
doi = {10.1016/j.anihpc.2004.04.001},
mrnumber = {2124163},
zbl = {1082.35129},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.04.001/}
}
TY - JOUR AU - Zhang, Ping AU - Zheng, Yuxi TI - Weak solutions to a nonlinear variational wave equation with general data JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 207 EP - 226 VL - 22 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2004.04.001/ DO - 10.1016/j.anihpc.2004.04.001 LA - en ID - AIHPC_2005__22_2_207_0 ER -
%0 Journal Article %A Zhang, Ping %A Zheng, Yuxi %T Weak solutions to a nonlinear variational wave equation with general data %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 207-226 %V 22 %N 2 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2004.04.001/ %R 10.1016/j.anihpc.2004.04.001 %G en %F AIHPC_2005__22_2_207_0
Zhang, Ping; Zheng, Yuxi. Weak solutions to a nonlinear variational wave equation with general data. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 207-226. doi: 10.1016/j.anihpc.2004.04.001
[1] , , Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511-547. | Zbl | MR
[2] , , Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987) 667-689. | Zbl | MR
[3] , Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS Regional Conf. Ser. in Math., vol. 74, Amer. Math. Soc., Providence, RI, 1990. | Zbl | MR
[4] , Microlocal defect measures, Comm. Partial Differential Equations 16 (1991) 1761-1794. | Zbl | MR
[5] , , , Singularities in a nonlinear variational wave equation, J. Differential Equations 129 (1996) 49-78. | Zbl | MR
[6] , , , Singularities and oscillations in a nonlinear variational wave equation, in: IMA, vol. 91, Springer, 1997. | Zbl | MR
[7] , , A family of nonlinear Klein-Gordon equations and their solutions, J. Math. Phys. 33 (1992) 2498-2503. | Zbl | MR
[8] , , Dynamics of director fields, SIAM J. Appl. Math. 51 (1991) 1498-1521. | Zbl | MR
[9] , , On a nonlinear hyperbolic variational equation I and II, Arch. Rational Mech. Anal. 129 (1995) 305-353, and 355-383. | Zbl
[10] , , On the 3-D axi-symmetric solutions to the compressible Navier-Stokes equations, J. Math. Pures Appl. (9) 82 (2003) 949-973. | Zbl | MR
[11] , , , Focusing at a point and absorption of nonlinear oscillations, Trans. Amer. Math. Soc. 347 (1995) 3921-3970. | Zbl | MR
[12] , Mathematical Topics in Fluid Mechanics, vol. 1, Incompressible Models, Lecture Series in Mathematics and its Applications, vol. 3, Clarendon Press, Oxford, 1996. | Zbl | MR
[13] , Mathematical Topics in Fluid Mechanics, vol. 2, Compressible Models, Lecture Series in Mathematics and its Applications, vol. 6, Clarendon Press, Oxford, 1998. | Zbl | MR
[14] , Dynamic instability of the liquid crystal director, in: (Ed.), Current Progress in Hyperbolic Systems, Contemp. Math., vol. 100, Amer. Math. Soc., Providence, RI, 1989, pp. 325-330. | Zbl | MR
[15] , Compensated compactness and applications to partial differential equations, in: (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Res. Notes Math., vol. 39, Pitman, 1979. | Zbl | MR
[16] , H-measures, a new approach for studying homogenisation oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburg Sect. A 115 (1990) 193-230. | Zbl | MR
[17] , Lectures on the Calculus of Variations and Optimal Control Theory, Saunders, Philadelphia, 1969. | Zbl | MR
[18] , , Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations 26 (2001) 381-420. | Zbl | MR
[19] , , Existence and uniqueness of solutions to an asymptotic equation of a variational wave equation with general data, Arch. Rational Mech. Anal. 155 (2000) 49-83. | Zbl | MR
[20] , , Singular and rarefactive solutions to a nonlinear variational wave equation, Chinese Ann. Math. Ser. B 22B (2000) 159-170. | Zbl | MR
[21] , , Weak solutions to a nonlinear variational wave equation, Arch. Rational Mech. Anal. 166 (2003) 303-319. | Zbl | MR
[22] , , New soliton equations for dipole chains, Phys. Rev. Lett. 68 (1992) 1180-1183.
Cité par Sources :





