Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
By Stathis Filippas, M. A. Herrero, Juan J.L Veláazquez. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2000
109 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/1aec52f44f96273201dec90bf7b8b5cbfbaf0777
How researchers see this paper
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In Applied Mathematics
- Hatem Zaag
- F. Merle
- Pavol Quittner
- Hiroshi Matano
- Yoshikazu Giga
- Carlos E. Kenig
- Yvan Martel
- Thomas Duyckaerts
In Computational Theory and Mathematics
- F. Merle
- Hatem Zaag
- Hiroshi Matano
- Pavol Quittner
- Yoshikazu Giga
- Carlos E. Kenig
- Ken Abe
- Nader Masmoudi
In Control and Systems Engineering
- Hatem Zaag
- F. Merle
- Hiroshi Matano
- Pavol Quittner
- Yoshikazu Giga
- B. Dodson
- Carlos E. Kenig
- Pierre Raphael
Citations in the corpus
- Infinite-time blow-up for the 3-dimensional energy-critical heat equation (2017, unknown): “1) is constructed, first formally predicted in [17].”
- Optimal Liouville theorems for superlinear parabolic problems (2020, background): “tant C which depends on the solution. Let us also mention that if p = pS, 3 ≤ n ≤ 6, and we allow sign-changing solution, then the blow-up may be of type II : This is indicated by formal arguments in [12] and proved in [30, 7, 8, 9, 17, 18]. Type II blow-up can also occur for positive radial and non”
- On Blow up at Space Infinity for Semilinear Heat Equations (2006, background): “[ 1 ], [9]. If one considers only radial solutions of (1) for supercritical p less than 1 + 4/(n − 4 − 2(n − 1)1/2 )o rn ≤ 10, then the estimate”
- On Nonexistence of type II blowup for a supercritical nonlinear heat equation (2004, background): “Regarding the critical case p = ps , Filippas, Herrero, and Velázquez [4] have proven the same result as Theorem 1.7 under the additional assumption that ∂u0/∂r ≤ 0, which we do not need.”
- Determination of the blow-up rate for a critical semilinear wave equation (2005, background): “The wave equation has no new blow-up rate at the critical case, unlike NLS where new blow-up rates appear at the critical case (with respect to the conformal invariance), see Merle and Raphaël [13], [12], [14], or the semilinear heat equation where we have new blow-up rates at the critical case (wit”