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Nonradial positive solutions for a biharmonic critical growth problem
Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions
1. | Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, United States |
References:
[1] |
M. Keel, H. F. Smith and C. D. Sogge, Almost global existence for some semilinear wave equations, J. Anal. Math., 87 (2002), 265-279.
doi: 10.1007/BF02868477. |
[2] |
M. Keel, H. F. Smith and C. D. Sogge, Global existence for a quasilinear wave equation outside of star-shaped domains, J. Funct. Anal., 189 (2002), 155-226.
doi: 10.1006/jfan.2001.3844. |
[3] |
S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), 321-332.
doi: 10.1002/cpa.3160380305. |
[4] |
S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math., 23 (1986), 293-326. |
[5] |
H. Koch, Mixed problems for fully nonlinear hyperbolic equations, Math. Z., 214 (1993), 9-42.
doi: 10.1007/BF02572388. |
[6] |
P. H. Lesky and R. Racke, Nonlinear wave equations in infinite waveguides, Comm. Partial Differential Equations, 28 (2003), 1265-1301.
doi: 10.1081/PDE-120024363. |
[7] |
J. Metcalfe and C. D. Sogge, Long time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods, SIAM J. Math. Anal., 38 (2006), 188-209.
doi: 10.1137/050627149. |
[8] |
J. Metcalfe, C. D. Sogge and A. Stewart, Nonlinear hyperbolic equations in infinite homogeneous waveguides, Comm. Partial Differential Equations, 30 (2005), 643-661.
doi: 10.1081/PDE-200059267. |
[9] |
J. Metcalfe and A. Stewart, Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions, Trans. Amer. Math. Soc., 360 (2008), 171-188.
doi: 10.1090/S0002-9947-07-04290-0. |
[10] |
C. S. Morawetz, Time decay for the nonlinear Klein-Gordon equations, Proc. Roy. Soc. Ser. A., 306 (1968), 291-296.
doi: 10.1098/rspa.1968.0151. |
[11] |
J. Sterbenz, Angular regularity and Strichartz estimates for the wave equation, with an appendix by I. Rodnianski, Int. Math. Res. Not., 2005, 187-231.
doi: 10.1155/IMRN.2005.187. |
[12] |
A. Stewart, "Existence Theorems for Some Nonlinear Hyperbolic Equations on a Waveguide," Ph. D. thesis, Johns Hopkins University, 2006. |
show all references
References:
[1] |
M. Keel, H. F. Smith and C. D. Sogge, Almost global existence for some semilinear wave equations, J. Anal. Math., 87 (2002), 265-279.
doi: 10.1007/BF02868477. |
[2] |
M. Keel, H. F. Smith and C. D. Sogge, Global existence for a quasilinear wave equation outside of star-shaped domains, J. Funct. Anal., 189 (2002), 155-226.
doi: 10.1006/jfan.2001.3844. |
[3] |
S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), 321-332.
doi: 10.1002/cpa.3160380305. |
[4] |
S. Klainerman, The null condition and global existence to nonlinear wave equations, Lect. Appl. Math., 23 (1986), 293-326. |
[5] |
H. Koch, Mixed problems for fully nonlinear hyperbolic equations, Math. Z., 214 (1993), 9-42.
doi: 10.1007/BF02572388. |
[6] |
P. H. Lesky and R. Racke, Nonlinear wave equations in infinite waveguides, Comm. Partial Differential Equations, 28 (2003), 1265-1301.
doi: 10.1081/PDE-120024363. |
[7] |
J. Metcalfe and C. D. Sogge, Long time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods, SIAM J. Math. Anal., 38 (2006), 188-209.
doi: 10.1137/050627149. |
[8] |
J. Metcalfe, C. D. Sogge and A. Stewart, Nonlinear hyperbolic equations in infinite homogeneous waveguides, Comm. Partial Differential Equations, 30 (2005), 643-661.
doi: 10.1081/PDE-200059267. |
[9] |
J. Metcalfe and A. Stewart, Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions, Trans. Amer. Math. Soc., 360 (2008), 171-188.
doi: 10.1090/S0002-9947-07-04290-0. |
[10] |
C. S. Morawetz, Time decay for the nonlinear Klein-Gordon equations, Proc. Roy. Soc. Ser. A., 306 (1968), 291-296.
doi: 10.1098/rspa.1968.0151. |
[11] |
J. Sterbenz, Angular regularity and Strichartz estimates for the wave equation, with an appendix by I. Rodnianski, Int. Math. Res. Not., 2005, 187-231.
doi: 10.1155/IMRN.2005.187. |
[12] |
A. Stewart, "Existence Theorems for Some Nonlinear Hyperbolic Equations on a Waveguide," Ph. D. thesis, Johns Hopkins University, 2006. |
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