Uniqueness and stability of regional blow-up in a porous-medium equation
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 6, pp. 927-960. 
@article{AIHPC_2002__19_6_927_0,
     author = {Cort\'azar, Carmen and del Pino, Manuel and Elgueta, Manuel},
     title = {Uniqueness and stability of regional blow-up in a porous-medium equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {927--960},
     publisher = {Elsevier},
     volume = {19},
     number = {6},
     year = {2002},
     mrnumber = {1939091},
     zbl = {1018.35062},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_6_927_0/}
}
TY  - JOUR
AU  - Cortázar, Carmen
AU  - del Pino, Manuel
AU  - Elgueta, Manuel
TI  - Uniqueness and stability of regional blow-up in a porous-medium equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2002
SP  - 927
EP  - 960
VL  - 19
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPC_2002__19_6_927_0/
LA  - en
ID  - AIHPC_2002__19_6_927_0
ER  - 
%0 Journal Article
%A Cortázar, Carmen
%A del Pino, Manuel
%A Elgueta, Manuel
%T Uniqueness and stability of regional blow-up in a porous-medium equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2002
%P 927-960
%V 19
%N 6
%I Elsevier
%U http://www.numdam.org/item/AIHPC_2002__19_6_927_0/
%G en
%F AIHPC_2002__19_6_927_0
Cortázar, Carmen; del Pino, Manuel; Elgueta, Manuel. Uniqueness and stability of regional blow-up in a porous-medium equation. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 6, pp. 927-960. http://www.numdam.org/item/AIHPC_2002__19_6_927_0/

[1] Cortázar C., Elgueta M., Felmer P., Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation, Comm. P.D.E. 21 (1996) 507-520. | MR | Zbl

[2] Cortázar C., Elgueta M., Felmer P., Uniqueness of positive solutions of Δu+f(u)=0 in RN, N≥3, Arch. Rat. Mech. Anal. 142 (1998) 127-141. | Zbl

[3] Cortázar C., Elgueta M., Felmer P., On a semilinear elliptic problem in RN with a non-lipschitzian nonlinearity, Adv. Differential Equations 1 (2) (1996) 199-218. | MR | Zbl

[4] Cortázar C., Del Pino M., Elgueta M., On the blow-up set for ut=Δum+um, m>1, Indiana Univ. Math. J. 47 (1998) 541-561. | Zbl

[5] Cortázar C., Del Pino M., Elgueta M., The problem of uniqueness of the limit in a semilinear heat equation, Comm. Partial Differential Equations 24 (1999) 2147-2172. | MR | Zbl

[6] Feireisl E., Petzeltova H., Convergence to a ground state as threshold phenomenos in nonlinear parabolic equations, Differential Integral Equations 10 (1997) 181-196. | MR | Zbl

[7] Feireisl E., Simondon F., Convergence for degenerate parabolic equations, J. Differential Equations 152 (2) (1999) 439-466. | MR | Zbl

[8] E. Feireisl, F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions, Preprint. | MR

[9] Fermanian Kammerer C., Merle F., Zaag H., Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view, Math. Ann. 317 (2000) 347-387. | MR | Zbl

[10] Fujita H., On the blowing-up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo 13 (1966) 109-124. | Zbl

[11] Galaktionov V., On a blow-up set for the quasilinear heat equation ut=(uσux)x+uσ+1, J. Differential Equations 101 (1993) 66-79. | Zbl

[12] Galaktionov V., Blow-up for quasilinear heat equations with critical Fujita's exponent, Proc. Roy. Soc. Edinburgh 124A (1994) 517-525. | MR | Zbl

[13] Galaktionov V., Peletier L.A., Asymptotic behaviour near finite-time extinction for the fast difussion equation, Arch. Rat. Mech. Anal. 139 (1997) 83-98. | MR | Zbl

[14] Galaktionov V., Vazquez J.L., Continuation of blowup solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math. 50 (1) (1997) 1-67. | MR | Zbl

[15] Giga Y., Kohn R., Characterizing blow-up using similarity variables, Indiana Univ. Math. J. 36 (1987) 1-40. | MR | Zbl

[16] Giga Y., Kohn R., Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math. 42 (1989) 845-884. | MR | Zbl

[17] Gui C., Symmetry of the blow-up set of a porous medium equation, Comm. Pure Appl. Math. 48 (1995) 471-500. | MR | Zbl

[18] Hale J., Raugel G., Convergence in gradient-like and applications, Z. Angew. Math. Phys. 43 (1992) 63-124. | MR | Zbl

[19] Haraux A., Polacik P., Convergence to a positive equilibrium for some nonlinear evolution equations in a ball, Acta Math. Univ. Comeniane 61 (1992) 129-141. | MR | Zbl

[20] Korevaar N., Mazzeo R., Pacard F., Schoen R., Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Mat. 135 (2) (1999) 233-272. | MR | Zbl

[21] Ladyzenskaja O.A., Solonnikov V.A., Ural'Ceva N.N., Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, 1968. | MR | Zbl

[22] Matano H., Nonincrease of the lap number of a solution for a one-dimensional semilinear parabolic equation, J. Fac. Sci. Univ. Tokyo 1A 29 (1982) 401-411. | MR | Zbl

[23] Ni W.-M., Takagi I., Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl

[24] Merle F., Zaag H., Stability of the blow-up profile for equations of the type ut=Δu+|u|p−1u, Duke Math. J. 86 (1997) 143-195. | Zbl

[25] Merle F., Zaag H., Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math. 51 (1998) 139-196. | MR | Zbl

[26] Polacik P., Rybakowski K.P., Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1996) 472-494. | MR | Zbl

[27] Samarskii A., Galaktionov V., Kurdyumov V., Mikhailov A., Blow-up in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987, in Russian.

[28] Simon L., Asymptotics for a class of non-linear evolution equations with applications to geometric problems, Ann. of Math. 118 (1983) 525-571. | MR | Zbl

[29] Velázquez J., Characterizing blow-up using similarity variables, Indiana Univ. Math. J. 42 (1993) 445-476. | MR | Zbl