Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications

Frank Merle[1]; Hatem Zaag[2]

  • [1] Université de Cergy-Pontoise
  • [2] École Normale Supérieure et Université de Cergy-Pontoise

Séminaire Équations aux dérivées partielles (1996-1997)

  • Volume: 1996-1997, page 1-8

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Merle, Frank, and Zaag, Hatem. "Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications." Séminaire Équations aux dérivées partielles 1996-1997 (1996-1997): 1-8. <http://eudml.org/doc/10923>.

@article{Merle1996-1997,
affiliation = {Université de Cergy-Pontoise; École Normale Supérieure et Université de Cergy-Pontoise},
author = {Merle, Frank, Zaag, Hatem},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-8},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications},
url = {http://eudml.org/doc/10923},
volume = {1996-1997},
year = {1996-1997},
}

TY - JOUR
AU - Merle, Frank
AU - Zaag, Hatem
TI - Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications
JO - Séminaire Équations aux dérivées partielles
PY - 1996-1997
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1996-1997
SP - 1
EP - 8
LA - eng
UR - http://eudml.org/doc/10923
ER -

References

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  1. Ball, J., Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford 28, 1977, pp. 473-486. Zbl0377.35037MR473484
  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. Zbl0806.35067MR1280993
  3. Bricmont, J., et Kupiainen, A., Universality in blow-up for nonlinear heat equations, Nonlinearity 7, 1994, pp. 539-575. Zbl0857.35018MR1267701
  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. Zbl0692.35013MR986159
  5. Filippas, S., et Kohn, R., Refined asymptotics for the blowup of u t - Δ u = u p , Comm. Pure Appl. Math. 45, 1992, pp. 821-869. Zbl0784.35010MR1164066
  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. Zbl0842.35006MR1359958
  7. Giga, Y., et Kohn, R., Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math. 42, 1989, pp. 845-884. Zbl0703.35020MR1003437
  8. Giga, Y., et Kohn, R., Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36, 1987, pp. 1-40. Zbl0601.35052MR876989
  9. Giga, Y., et Kohn, R., Asymptotically self-similar blowup of semilinear heat equations, Comm. Pure Appl. Math. 38, 1985, pp. 297-319. Zbl0585.35051MR784476
  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. Zbl0813.35007MR1220032
  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. Zbl0767.35036MR1171974
  12. Merle, F., et Zaag, H., Refined uniform estimates at blow-up and applications for nonlinear heat equations, en préparation. Zbl0926.35024
  13. Merle, F.,et Zaag, H., Optimal estimates for blow-up rate and behavior for nonlinear heat equations, prépublication. Zbl0899.35044
  14. Merle, F., et Zaag, H., Stability of blow-up profile for equation of the type u t = Δ u + | u | p - 1 u , Duke Math. J. 86, 1997, pp. 143-195. Zbl0872.35049MR1427848
  15. Zaag, H., Blow-up results for vector valued nonlinear heat equations with no gradient structure, Ann. Inst. Henri Poincaré, à paraî tre. Zbl0902.35050MR1643389

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