Complete blow up and global behaviour of solutions of u t - Δ u = g ( u )

Yvan Martel

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 6, page 687-723
  • ISSN: 0294-1449

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Martel, Yvan. "Complete blow up and global behaviour of solutions of $u_t - \Delta u = g (u)$." Annales de l'I.H.P. Analyse non linéaire 15.6 (1998): 687-723. <http://eudml.org/doc/78453>.

@article{Martel1998,
author = {Martel, Yvan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear heat equation; blow up in infinite time; convergence rate},
language = {eng},
number = {6},
pages = {687-723},
publisher = {Gauthier-Villars},
title = {Complete blow up and global behaviour of solutions of $u_t - \Delta u = g (u)$},
url = {http://eudml.org/doc/78453},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Martel, Yvan
TI - Complete blow up and global behaviour of solutions of $u_t - \Delta u = g (u)$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 6
SP - 687
EP - 723
LA - eng
KW - nonlinear heat equation; blow up in infinite time; convergence rate
UR - http://eudml.org/doc/78453
ER -

References

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  1. [1] P. Baras and L. Cohen, Complete blow after Tmax for the solution of a semilinear heat equation, J. Funct. Anal., Vol. 71, 1987, pp. 142-174. Zbl0653.35037MR879705
  2. [2] P. Baras and M. Pierre, Critère d'existence de solutions positives pour des equations semi-linéaires non monotones, Ann. Inst. Henri Poincaré, Vol. 2, 1985, pp. 185-212. Zbl0599.35073MR797270
  3. [3] H. Brezis, T. Cazenave, Y. Martel and A. Ramiandrisoa, Blow up for ut - Δu = g(u) revisited, Adv. Diff. Eq., Vol. 1, 1996, pp. 73-90. Zbl0855.35063MR1357955
  4. [4] H. Fujita, On the nonlinear equations Δu + eu = 0 and ∂u/ ∂t = Δu + eu, Bull. Amer. Math. Soc., Vol. 75, 1969, pp. 132-135. Zbl0216.12101MR239258
  5. [5] V.A. Galaktionov and J.L. Vazquez, Continuation of blow up solutions of nonlinear heat equations in several space dimensions, to appear. Zbl0874.35057
  6. [6] A.A. Lacey and D.E. Tzanetis, Global, unbounded solutions to a parabolic equation, J. Diff. Eq., Vol. 101, 1993, pp. 80-102. Zbl0799.35123MR1199484
  7. [7] Y. Martel, Uniqueness of weak extremal solutions of nonlinear elliptic problems, to appear in Houston Journal of Math., 1997. Zbl0884.35037MR1688823
  8. [8] P. Mironescu and V.D. Radulescu, The study of a bifurcation problem associated to an asymptotically linear function, Nonlinear Analysis TMA, Vol. 26, 1996, pp. 857-875. Zbl0842.35008MR1362758
  9. [9] W.-M. Ni, P.E. Sacks and J. Tavantzis, On the asymptotic behavior of solutions of certain quasilinear parabolic equations, J. Diff. Eq., Vol. 54, 1984, pp. 97-120. Zbl0565.35053MR756548

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