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
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top- R. J. DiPerna and P. L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98(1989), pp. 511–547. Zbl0696.34049MR1022305
- 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. Zbl0626.35059MR877643
- P. Gerard, Microlocal defect measures, Comm. in Partial Differential Equations, 16 (1991), pp. 1761–1794. Zbl0770.35001MR1135919
- 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
- J. K. Hunter and R. A. Saxton, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498–1521. Zbl0761.35063MR1135995
- 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
- 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
- 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
- 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
- Ping Zhang and Yuxi Zheng, Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations, 26 (2001), pp. 381-420. Zbl0989.35112MR1842038
- 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
- Ping Zhang and Yuxi Zheng, Weak solutions to a nonlinear variational wave equation, Arch. Rat. Mech. Anal., 166 (2003), pp. 303-319. Zbl1029.35173MR1961443
- 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