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Séminaire Équations aux dérivées partielles (Polytechnique)Table of contents for this volume | Previous article | Next articleFrank Merle; Hatem Zaag Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications Séminaire Équations aux dérivées partielles (Polytechnique) (1996-1997), Exp. No. 19, 8 p. Article PDF | Reviews Zbl 1069.35505 Bibliography [2] Bricmont, J., Kupiainen, A., et Lin, G., Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Comm. Pure Appl. Math. 47, 1994, pp. 893-922. MR 1280993 | Zbl 0806.35067 [3] Bricmont, J., et Kupiainen, A., Universality in blow-up for nonlinear heat equations, Nonlinearity 7, 1994, pp. 539-575. MR 1267701 | Zbl 0857.35018 [4] Chen, X., Y., et Matano, H., Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations, J. Diff. Eqns. 78, 1989, pp. 160-190. MR 986159 | Zbl 0692.35013 [5] Filippas, S., et Kohn, R., Refined asymptotics for the blowup of $u_t-\Delta u=u^p$, Comm. Pure Appl. Math. 45, 1992, pp. 821-869. MR 1164066 | Zbl 0784.35010 [6] Galaktionov, V., A., et Vazquez, J., L., Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations, Math. Ann. 303, 1995, pp. 741-769. MR 1359958 | Zbl 0842.35006 [7] Giga, Y., et Kohn, R., Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math. 42, 1989, pp. 845-884. MR 1003437 | Zbl 0703.35020 [8] Giga, Y., et Kohn, R., Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36, 1987, pp. 1-40. MR 876989 | Zbl 0601.35052 [9] Giga, Y., et Kohn, R., Asymptotically self-similar blowup of semilinear heat equations, Comm. Pure Appl. Math. 38, 1985, pp. 297-319. MR 784476 | Zbl 0585.35051 [10] Herrero, M.A, et Velazquez, J.J.L., Blow-up behavior of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poin- caré 10, 1993, pp. 131-189. Numdam | MR 1220032 | Zbl 0813.35007 [11] Herrero, M.A, et Velazquez, J.J.L., Flat blow-up in one-dimensional semilinear heat equations, Differential and Integral eqns. 5, 1992, pp. 973-997. MR 1171974 | Zbl 0767.35036 [12] Merle, F., et Zaag, H., Refined uniform estimates at blow-up and applications for nonlinear heat equations, en préparation. Zbl 0926.35024 [13] Merle, F.,et Zaag, H., Optimal estimates for blow-up rate and behavior for nonlinear heat equations, prépublication. Zbl 0899.35044 [14] Merle, F., et Zaag, H., Stability of blow-up profile for equation of the type $u_t = \Delta u + |u|^{p-1}u$, Duke Math. J. 86, 1997, pp. 143-195. Article | MR 1427848 | Zbl 0872.35049 [15] Zaag, H., Blow-up results for vector valued nonlinear heat equations with no gradient structure, Ann. Inst. Henri Poincaré, à paraî tre. Numdam | MR 1643389 | Zbl 0902.35050 |
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