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Blowup of solutions to semilinear wave equations with nonzero initial data
1.  Department of Mathematics, Hokkaido University, Sapporo, 0600810, Japan 
H. Takamura [13] obtained the blowup result for the case where $f\equiv0$ and $g\not\equiv0$. Our purpose in this paper is to show the blowup result for the case where the both initial data do not vanish identically.
References:
[1] 
R. Agemi, Blowup of solutions to nonlinear wave equations in two space dimensions,, Manuscripta Math., 73 (1991), 153. Google Scholar 
[2] 
R. T. Glassey, MathReview to "Global behavior of solutions to nonlinear wave equations in three space dimensions" of Sideris,, Comm. Partial Differential Equations (1983)., (1983). Google Scholar 
[3] 
K. Hidano, Initial value problem of semilinear wave equations in three space dimensions,, Nonlinear Anal., 26 (1996), 941. Google Scholar 
[4] 
K. Hidano and K. Tsutaya, Global existence and asymptotic behavior of solutions for nonlinear wave equations,, Indiana Univ. Math. J., 44 (1995), 1273. Google Scholar 
[5] 
K. Hidano, C. Wang and K. Yokoyama, The Glassey conjecture with radially symmetric data,, Journal de Math ématiques Pures et Appliqu ées (9), 98 (2012), 518. Google Scholar 
[6] 
F. John, Blowup of solutions for quasilinear wave equations in three space dimensions,, Comm. Pure Appl. Math., 34 (1981), 29. Google Scholar 
[7] 
H. Kubo, Blowup of solutions to semilinear wave equations with initial data of slow decay in low space dimensions,, Differential and Integral Equations., 7 (1994), 315. Google Scholar 
[8] 
K. Masuda, Blowup solutions for quasilinear wave equations in two space dimensions,, Lecture Notes in Num. Appl. Anal., 6 (1983), 87. Google Scholar 
[9] 
M. A. Rammaha, Finitetime blowup for nonlinear wave equations in high dimensions,, Comm. Partial Differential Equations, 12 (1987), 677. Google Scholar 
[10] 
M. A. Rammaha, H. Takamura, H. Uesaka and K. Wakasa, BlowUp of Positive Solutions to Wave Equations in High Space Dimensions,, to appear in Differential and Integral Equations, (). Google Scholar 
[11] 
J. Schaeffer, Finitetime blowup for $u_{t t}\Delta u=H(u_r,u_t)$ in two space dimensions,, Comm. Partial Differential Equations, 11 (1986), 513. Google Scholar 
[12] 
T. C. Sideris, Global behavior of solutions to nonlinear wave equations in three space dimensions,, Comm. Partial Differential Equations, 8 (1983), 1219. Google Scholar 
[13] 
H. Takamura, Blowup for semilinear wave equations with slowly decaying data in high dimensions,, Differential Integral Equations, 8 (1995), 647. Google Scholar 
[14] 
N. Tzvetkov, Existence of global solutions to nonlinear massless Dirac system and wave equations with small data,, Tsukuba Math. J., 22 (1998), 198. Google Scholar 
[15] 
Y. Zhou, Blow up of solutions to the Cauchy problem for nonlinear wave equations,, Chin. Ann. Math. Ser.B, 22 (2001), 275. Google Scholar 
show all references
References:
[1] 
R. Agemi, Blowup of solutions to nonlinear wave equations in two space dimensions,, Manuscripta Math., 73 (1991), 153. Google Scholar 
[2] 
R. T. Glassey, MathReview to "Global behavior of solutions to nonlinear wave equations in three space dimensions" of Sideris,, Comm. Partial Differential Equations (1983)., (1983). Google Scholar 
[3] 
K. Hidano, Initial value problem of semilinear wave equations in three space dimensions,, Nonlinear Anal., 26 (1996), 941. Google Scholar 
[4] 
K. Hidano and K. Tsutaya, Global existence and asymptotic behavior of solutions for nonlinear wave equations,, Indiana Univ. Math. J., 44 (1995), 1273. Google Scholar 
[5] 
K. Hidano, C. Wang and K. Yokoyama, The Glassey conjecture with radially symmetric data,, Journal de Math ématiques Pures et Appliqu ées (9), 98 (2012), 518. Google Scholar 
[6] 
F. John, Blowup of solutions for quasilinear wave equations in three space dimensions,, Comm. Pure Appl. Math., 34 (1981), 29. Google Scholar 
[7] 
H. Kubo, Blowup of solutions to semilinear wave equations with initial data of slow decay in low space dimensions,, Differential and Integral Equations., 7 (1994), 315. Google Scholar 
[8] 
K. Masuda, Blowup solutions for quasilinear wave equations in two space dimensions,, Lecture Notes in Num. Appl. Anal., 6 (1983), 87. Google Scholar 
[9] 
M. A. Rammaha, Finitetime blowup for nonlinear wave equations in high dimensions,, Comm. Partial Differential Equations, 12 (1987), 677. Google Scholar 
[10] 
M. A. Rammaha, H. Takamura, H. Uesaka and K. Wakasa, BlowUp of Positive Solutions to Wave Equations in High Space Dimensions,, to appear in Differential and Integral Equations, (). Google Scholar 
[11] 
J. Schaeffer, Finitetime blowup for $u_{t t}\Delta u=H(u_r,u_t)$ in two space dimensions,, Comm. Partial Differential Equations, 11 (1986), 513. Google Scholar 
[12] 
T. C. Sideris, Global behavior of solutions to nonlinear wave equations in three space dimensions,, Comm. Partial Differential Equations, 8 (1983), 1219. Google Scholar 
[13] 
H. Takamura, Blowup for semilinear wave equations with slowly decaying data in high dimensions,, Differential Integral Equations, 8 (1995), 647. Google Scholar 
[14] 
N. Tzvetkov, Existence of global solutions to nonlinear massless Dirac system and wave equations with small data,, Tsukuba Math. J., 22 (1998), 198. Google Scholar 
[15] 
Y. Zhou, Blow up of solutions to the Cauchy problem for nonlinear wave equations,, Chin. Ann. Math. Ser.B, 22 (2001), 275. Google Scholar 
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