We consider the energy critical semilinear heat equation
Nous considérons l'équation de la chaleur énergie critique
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@article{CRMATH_2017__355_1_65_0, author = {Collot, Charles and Merle, Frank and Rapha\"el, Pierre}, title = {Stability of {ODE} blow-up for the energy critical semilinear heat equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {65--79}, publisher = {Elsevier}, volume = {355}, number = {1}, year = {2017}, doi = {10.1016/j.crma.2016.10.020}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.crma.2016.10.020/} }
TY - JOUR AU - Collot, Charles AU - Merle, Frank AU - Raphaël, Pierre TI - Stability of ODE blow-up for the energy critical semilinear heat equation JO - Comptes Rendus. Mathématique PY - 2017 SP - 65 EP - 79 VL - 355 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2016.10.020/ DO - 10.1016/j.crma.2016.10.020 LA - en ID - CRMATH_2017__355_1_65_0 ER -
%0 Journal Article %A Collot, Charles %A Merle, Frank %A Raphaël, Pierre %T Stability of ODE blow-up for the energy critical semilinear heat equation %J Comptes Rendus. Mathématique %D 2017 %P 65-79 %V 355 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2016.10.020/ %R 10.1016/j.crma.2016.10.020 %G en %F CRMATH_2017__355_1_65_0
Collot, Charles; Merle, Frank; Raphaël, Pierre. Stability of ODE blow-up for the energy critical semilinear heat equation. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 65-79. doi : 10.1016/j.crma.2016.10.020. https://www.numdam.org/articles/10.1016/j.crma.2016.10.020/
[1] Fourier Analysis and Nonlinear Partial Differential Equations, vol. 343, Springer Science Business, Media, 2011
[2] A nonlinear heat equation with singular initial data, J. Anal. Math., Volume 68 (1996) no. 1, pp. 277-304
[3] C. Collot, F. Merle, P. Raphaël, Dynamics near the ground state for the energy critical nonlinear heat equation in large dimension, preprint, 2016.
[4] Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view, Math. Ann., Volume 317 (2000) no. 2, pp. 347-387
[5] Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity, Proc. R. Soc. Lond. A, Volume 456 (2000) no. 2004, pp. 2957-2982
[6] On elliptic equations related to self-similar solutions for nonlinear heat equations, Hiroshima Math. J., Volume 16 (1986) no. 3, pp. 539-552
[7] Asymptotically self-similar blow-up of semilinear heat equations, Commun. Pure Appl. Math., Volume 38 (1985) no. 3, pp. 297-319
[8] Characterizing blowup using similarity variables, Indiana Univ. Math. J., Volume 36 (1987), pp. 1-40
[9] Nondegeneracy of blowup for semilinear heat equations, Commun. Pure Appl. Math., Volume 42 (1989) no. 6, pp. 845-884
[10] Blow up rate for semilinear heat equations with subcritical nonlinearity, Indiana Univ. Math. J., Volume 53 (2004) no. 2, pp. 483-514
[11] Optimal estimates for blowup rate and behavior for nonlinear heat equations, Commun. Pure Appl. Math., Volume 51 (1998) no. 2, pp. 139-196
[12] A Liouville theorem for vector-valued nonlinear heat equations and applications, Math. Ann., Volume 316 (2000) no. 1, pp. 103-137
[13] Superlinear Parabolic Problems: Blow-Up, Global Existence and Steady States, Springer Science and Business Media, 2007
[14] Type II blow-up for the four dimensional energy critical semi linear heat equation, J. Funct. Anal., Volume 263 (2012) no. 12, pp. 3922-3983
[15] Local existence and nonexistence for semilinear parabolic equations in Lp, Indiana Univ. Math. J., Volume 29 (1980) no. 1, pp. 79-102
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