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In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any $p>1$. We also get the blow-up rate of the derivative under the condition $1<p<1+\frac{4}{N-1}$ for $N\geq2$ or $1<p<5$ for $N=1$.
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참고문헌 (10)
참고문헌 신청
C. Antonini / 2001 / Optimal bounds on positive blow-up solutions for a semilinear wave equation / Internat. Math. Res. Notices 21 (21) : 1141 ~ 1167
F. Merle / 2003 / Determination of the blow-up rate for the semilinear wave equa-tion / Amer. J. Math 125 (5) : 1147 ~ 1164
F. Merle / 2005 / Determination of the blow-up rate for a critical semilinear wave equation / Math. Ann 331 (2) : 395 ~ 416
F. Merle / 2005 / On growth rate near the blow-up surface for semilinear wave equations / Int. Math. Res. Not 19 (19) : 1127 ~ 1155
L. A. Caffarelli / 1986 / The blow-up boundary for nonlinear wave equations / Trans. Amer. Math. Soc 297 (1) : 223 ~ 241
F. Merle / 2003 / Determination of the blow-up rate for the semilinear wave equa-tion / Amer. J. Math 125 (5) : 1147 ~ 1164
F. Merle / 2005 / Determination of the blow-up rate for a critical semilinear wave equation / Math. Ann 331 (2) : 395 ~ 416
F. Merle / 2005 / On growth rate near the blow-up surface for semilinear wave equations / Int. Math. Res. Not 19 (19) : 1127 ~ 1155
L. A. Caffarelli / 1986 / The blow-up boundary for nonlinear wave equations / Trans. Amer. Math. Soc 297 (1) : 223 ~ 241
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