Complete blow up and global behaviour of solutions of u t -Δu=g(u)
Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 6, p. 687-723
@article{AIHPC_1998__15_6_687_0,
     author = {Martel, Yvan},
     title = {Complete blow up and global behaviour of solutions of $u\_t - \Delta u = g (u)$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {6},
     year = {1998},
     pages = {687-723},
     zbl = {0914.35057},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1998__15_6_687_0}
}
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, Volume 15 (1998) no. 6, pp. 687-723. http://www.numdam.org/item/AIHPC_1998__15_6_687_0/

[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. | MR 879705 | Zbl 0653.35037

[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. | Numdam | MR 797270 | Zbl 0599.35073

[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. | MR 1357955 | Zbl 0855.35063

[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. | MR 239258 | Zbl 0216.12101

[5] V.A. Galaktionov and J.L. Vazquez, Continuation of blow up solutions of nonlinear heat equations in several space dimensions, to appear.

[6] A.A. Lacey and D.E. Tzanetis, Global, unbounded solutions to a parabolic equation, J. Diff. Eq., Vol. 101, 1993, pp. 80-102. | MR 1199484 | Zbl 0799.35123

[7] Y. Martel, Uniqueness of weak extremal solutions of nonlinear elliptic problems, to appear in Houston Journal of Math., 1997. | MR 1688823 | Zbl 0884.35037

[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. | MR 1362758 | Zbl 0842.35008

[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. | MR 756548 | Zbl 0565.35053