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

How to cite

top

Cortázar, 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. [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. [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. [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. [4] Cortázar C., del Pino M., Elgueta M., On the blow-up set for ut=Δum+um, m&gt;1, Indiana Univ. Math. J.47 (1998) 541-561. Zbl0916.35056
  5. [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. [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. [7] Feireisl E., Simondon F., Convergence for degenerate parabolic equations, J. Differential Equations152 (2) (1999) 439-466. Zbl0928.35086MR1674569
  8. [8] E. Feireisl, F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions, Preprint. Zbl0977.35069MR1800136
  9. [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. [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. [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. [12] Galaktionov V., Blow-up for quasilinear heat equations with critical Fujita's exponent, Proc. Roy. Soc. Edinburgh124A (1994) 517-525. Zbl0808.35053MR1286917
  13. [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. [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. [15] Giga Y., Kohn R., Characterizing blow-up using similarity variables, Indiana Univ. Math. J.36 (1987) 1-40. Zbl0601.35052MR876989
  16. [16] Giga Y., Kohn R., Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math.42 (1989) 845-884. Zbl0703.35020MR1003437
  17. [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. [18] Hale J., Raugel G., Convergence in gradient-like and applications, Z. Angew. Math. Phys.43 (1992) 63-124. Zbl0751.58033MR1149371
  19. [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. [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. [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. [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. [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. [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. [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. [26] Polacik P., Rybakowski K.P., Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations124 (1996) 472-494. Zbl0845.35054MR1370152
  27. [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. [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. [29] Velázquez J., Characterizing blow-up using similarity variables, Indiana Univ. Math. J.42 (1993) 445-476. Zbl0802.35073MR1237055

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.