Uniqueness and stability of regional blow-up in a porous-medium equation
Carmen Cortázar; Manuel del Pino; Manuel Elgueta
Annales de l'I.H.P. Analyse non linéaire (2002)
- Volume: 19, Issue: 6, page 927-960
- ISSN: 0294-1449
Access Full Article
topHow to cite
topCortázar, Carmen, del Pino, Manuel, and Elgueta, Manuel. "Uniqueness and stability of regional blow-up in a porous-medium equation." Annales de l'I.H.P. Analyse non linéaire 19.6 (2002): 927-960. <http://eudml.org/doc/78567>.
@article{Cortázar2002,
author = {Cortázar, Carmen, del Pino, Manuel, Elgueta, Manuel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {spherical hot spots; unique blow-up profile; blow-up; porous-medium equation},
language = {eng},
number = {6},
pages = {927-960},
publisher = {Elsevier},
title = {Uniqueness and stability of regional blow-up in a porous-medium equation},
url = {http://eudml.org/doc/78567},
volume = {19},
year = {2002},
}
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
PB - Elsevier
VL - 19
IS - 6
SP - 927
EP - 960
LA - eng
KW - spherical hot spots; unique blow-up profile; blow-up; porous-medium equation
UR - http://eudml.org/doc/78567
ER -
References
top- [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. Zbl0854.35033MR1387457
- [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. Zbl0912.35059
- [3] Cortázar C., Elgueta M., Felmer P., On a semilinear elliptic problem in RN with a non-lipschitzian nonlinearity, Adv. Differential Equations1 (2) (1996) 199-218. Zbl0845.35031MR1364001
- [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. Zbl0916.35056
- [5] Cortázar C., del Pino M., Elgueta M., The problem of uniqueness of the limit in a semilinear heat equation, Comm. Partial Differential Equations24 (1999) 2147-2172. Zbl0940.35107MR1720758
- [6] Feireisl E., Petzeltova H., Convergence to a ground state as threshold phenomenos in nonlinear parabolic equations, Differential Integral Equations10 (1997) 181-196. Zbl0879.35023MR1424805
- [7] Feireisl E., Simondon F., Convergence for degenerate parabolic equations, J. Differential Equations152 (2) (1999) 439-466. Zbl0928.35086MR1674569
- [8] E. Feireisl, F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions, Preprint. Zbl0977.35069MR1800136
- [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. Zbl0971.35038MR1764243
- [10] Fujita H., On the blowing-up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo13 (1966) 109-124. Zbl0163.34002
- [11] Galaktionov V., On a blow-up set for the quasilinear heat equation ut=(uσux)x+uσ+1, J. Differential Equations101 (1993) 66-79. Zbl0802.35065
- [12] Galaktionov V., Blow-up for quasilinear heat equations with critical Fujita's exponent, Proc. Roy. Soc. Edinburgh124A (1994) 517-525. Zbl0808.35053MR1286917
- [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. Zbl0885.35058MR1475779
- [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. Zbl0874.35057MR1423231
- [15] Giga Y., Kohn R., Characterizing blow-up using similarity variables, Indiana Univ. Math. J.36 (1987) 1-40. Zbl0601.35052MR876989
- [16] Giga Y., Kohn R., Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math.42 (1989) 845-884. Zbl0703.35020MR1003437
- [17] Gui C., Symmetry of the blow-up set of a porous medium equation, Comm. Pure Appl. Math.48 (1995) 471-500. Zbl0827.35014MR1329829
- [18] Hale J., Raugel G., Convergence in gradient-like and applications, Z. Angew. Math. Phys.43 (1992) 63-124. Zbl0751.58033MR1149371
- [19] Haraux A., Polacik P., Convergence to a positive equilibrium for some nonlinear evolution equations in a ball, Acta Math. Univ. Comeniane61 (1992) 129-141. Zbl0824.35011MR1205867
- [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. Zbl0958.53032MR1666838
- [21] Ladyzenskaja O.A., Solonnikov V.A., Ural'ceva N.N., Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, 1968. Zbl0174.15403MR241822
- [22] Matano H., Nonincrease of the lap number of a solution for a one-dimensional semilinear parabolic equation, J. Fac. Sci. Univ. Tokyo 1A29 (1982) 401-411. Zbl0496.35011MR672070
- [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. Zbl0796.35056MR1219814
- [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. Zbl0872.35049
- [25] Merle F., Zaag H., Optimal estimates for blowup rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math.51 (1998) 139-196. Zbl0899.35044MR1488298
- [26] Polacik P., Rybakowski K.P., Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations124 (1996) 472-494. Zbl0845.35054MR1370152
- [27] Samarskii A., Galaktionov V., Kurdyumov V., Mikhailov A., Blow-up in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987, in Russian. Zbl1020.35001
- [28] Simon L., Asymptotics for a class of non-linear evolution equations with applications to geometric problems, Ann. of Math.118 (1983) 525-571. Zbl0549.35071MR727703
- [29] Velázquez J., Characterizing blow-up using similarity variables, Indiana Univ. Math. J.42 (1993) 445-476. Zbl0802.35073MR1237055
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.