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Blow-up rate for the semi-linear wave equation in bounded domain

Chuangchuang Liang|Pengchao Wang
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회보 (Bulletin of the KMS)|제52권 제1호|pp. 173-182

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키워드

blow-up ratesemi-linear wave equationbounded domain
주제분류수학

초록

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 $N=1$.

Abstract

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 $N=1$.

참고문헌 (10)

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  2. C. Antonini, "Optimal bounds on positive blow-up solutions for a semilinear wave equation", Internat. Math. Res. Notices, 21(21), pp.1141~1167 (2001)
  3. P. Biz´on, "On blowup for semilinear wave equations with a focusing nonlinearity", Nonlinearity, 17(6), pp.2187~2201 (2004)
  4. L. A. Caffarelli, "The blow-up boundary for nonlinear wave equations", Trans. Amer. Math. Soc, 297(1), pp.223~241 (1986)
  5. "Blow-up results for semilinear wave equations in the super-conformal case"[URL]
  6. S. Kichenassamy, "Blow-up surfaces for nonlinear wave equations. I", Comm. Partial Differential Equations, 18(3-4), pp.431~452 (1993)
  7. S. Kichenassamy, "Blow-up surfaces for nonlinear wave equations. II", Comm. Partial Differential Equations, 18(11), pp.1869~1899 (1993)
  8. F. Merle, "Determination of the blow-up rate for the semilinear wave equa-tion", Amer. J. Math, 125(5), pp.1147~1164 (2003)
  9. F. Merle, "Determination of the blow-up rate for a critical semilinear wave equation", Math. Ann, 331(2), pp.395~416 (2005)
  10. F. Merle, "On growth rate near the blow-up surface for semilinear wave equations", Int. Math. Res. Not, 19(19), pp.1127~1155 (2005)

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