@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] 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] Uniqueness of positive solutions of Δu+f(u)=0 in RN, N≥3, Arch. Rat. Mech. Anal. 142 (1998) 127-141. | Zbl
, , ,[3] On a semilinear elliptic problem in RN with a non-lipschitzian nonlinearity, Adv. Differential Equations 1 (2) (1996) 199-218. | MR | Zbl
, , ,[4] On the blow-up set for ut=Δum+um, m>1, Indiana Univ. Math. J. 47 (1998) 541-561. | Zbl
, , ,[5] The problem of uniqueness of the limit in a semilinear heat equation, Comm. Partial Differential Equations 24 (1999) 2147-2172. | MR | Zbl
, , ,[6] Convergence to a ground state as threshold phenomenos in nonlinear parabolic equations, Differential Integral Equations 10 (1997) 181-196. | MR | Zbl
, ,[7] 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] 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] 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] On a blow-up set for the quasilinear heat equation ut=(uσux)x+uσ+1, J. Differential Equations 101 (1993) 66-79. | Zbl
,[12] Blow-up for quasilinear heat equations with critical Fujita's exponent, Proc. Roy. Soc. Edinburgh 124A (1994) 517-525. | MR | Zbl
,[13] Asymptotic behaviour near finite-time extinction for the fast difussion equation, Arch. Rat. Mech. Anal. 139 (1997) 83-98. | MR | Zbl
, ,[14] Continuation of blowup solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math. 50 (1) (1997) 1-67. | MR | Zbl
, ,[15] Characterizing blow-up using similarity variables, Indiana Univ. Math. J. 36 (1987) 1-40. | MR | Zbl
, ,[16] Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math. 42 (1989) 845-884. | MR | Zbl
, ,[17] Symmetry of the blow-up set of a porous medium equation, Comm. Pure Appl. Math. 48 (1995) 471-500. | MR | Zbl
,[18] Convergence in gradient-like and applications, Z. Angew. Math. Phys. 43 (1992) 63-124. | MR | Zbl
, ,[19] Convergence to a positive equilibrium for some nonlinear evolution equations in a ball, Acta Math. Univ. Comeniane 61 (1992) 129-141. | MR | Zbl
, ,[20] Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Mat. 135 (2) (1999) 233-272. | MR | Zbl
, , , ,[21] Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, 1968. | MR | Zbl
, , ,[22] 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] Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl
, ,[24] 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] Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math. 51 (1998) 139-196. | MR | Zbl
, ,[26] Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1996) 472-494. | MR | Zbl
, ,[27] Blow-up in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987, in Russian.
, , , ,[28] Asymptotics for a class of non-linear evolution equations with applications to geometric problems, Ann. of Math. 118 (1983) 525-571. | MR | Zbl
,[29] Characterizing blow-up using similarity variables, Indiana Univ. Math. J. 42 (1993) 445-476. | MR | Zbl
,