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  • Journées équations aux dérivées partielles
  • Year 2004
  • article no. 12
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On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation
Ping Zhang1; Yuxi Zheng2
1 Academy of Mathematics and System Sciences, CAS, Beijing 100080, China
2 Department of Mathematics, Penn State University, PA 16802
Journées équations aux dérivées partielles (2004), article no. 12, 12 p.
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MR   Zbl
DOI: 10.5802/jedp.12
Author's affiliations:
Ping Zhang 1; Yuxi Zheng 2

1 Academy of Mathematics and System Sciences, CAS, Beijing 100080, China
2 Department of Mathematics, Penn State University, PA 16802
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@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/}
}
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DO  - 10.5802/jedp.12
LA  - en
ID  - JEDP_2004____A12_0
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%0 Journal Article
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%J Journées équations aux dérivées partielles
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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/
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[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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