On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation

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

Journées Équations aux dérivées partielles (2004)

  • page 1-12
  • ISSN: 0752-0360

How to cite

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Zhang, Ping, and Zheng, Yuxi. "On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation." Journées Équations aux dérivées partielles (2004): 1-12. <http://eudml.org/doc/10591>.

@article{Zhang2004,
affiliation = {Academy of Mathematics and System Sciences, CAS, Beijing 100080, China; Department of Mathematics, Penn State University, PA 16802},
author = {Zhang, Ping, Zheng, Yuxi},
journal = {Journées Équations aux dérivées partielles},
keywords = {existence; regularity properties},
language = {eng},
month = {6},
pages = {1-12},
publisher = {Groupement de recherche 2434 du CNRS},
title = {On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation},
url = {http://eudml.org/doc/10591},
year = {2004},
}

TY - JOUR
AU - Zhang, Ping
AU - Zheng, Yuxi
TI - On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation
JO - Journées Équations aux dérivées partielles
DA - 2004/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 12
LA - eng
KW - existence; regularity properties
UR - http://eudml.org/doc/10591
ER -

References

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  3. P. Gerard, Microlocal defect measures, Comm. in Partial Differential Equations, 16 (1991), pp. 1761–1794. Zbl0770.35001MR1135919
  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. Zbl0879.35107MR1400796
  5. J. K. Hunter and R. A. Saxton, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498–1521. Zbl0761.35063MR1135995
  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. Zbl0834.35085
  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. Zbl0857.35087MR1297533
  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. Zbl0908.76004MR1637634
  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. Zbl0774.35008MR1069518
  10. Ping Zhang and Yuxi Zheng, Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations, 26 (2001), pp. 381-420. Zbl0989.35112MR1842038
  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. Zbl0982.35062MR1799274
  12. Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation, Arch. Rat. Mech. Anal., 166 (2003), pp. 303-319. Zbl1029.35173MR1961443
  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 ). Zbl1082.35129MR2124163

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