Asymptotically self-similar global solutions of a general semilinear heat equation

Mathematische Annalen

Volumn 321, Issue 1, 2001, Pages 131-155

  Snoussi, Seifeddine ^a   Tayachi, Slim ^b   Weissler, Fred B ^c  

^a UNIVERSITY OF TUNIS   (Tunisia)

^b FACULTÉ DES SCIENCES DE TUNIS   (Tunisia)

^c UNIVERSITÉ PARIS 13   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035601963     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004498     Document Type: Article

References (29)

1. M. Cannone, A generalization of a theorem by Kato on Navier-Stokes equations, Rev. Mat. Ib., 13 (1997), 515-541.
2. 3, Commun. Partial Differential Equations, 21 (1996), 179-193.
3. T. Cazenave and F. B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z., 228 (1998), 83-120.
4. T. Cazenave and F. B. Weissler, More self-similar solutions of the nonlinear Schrödinger equation, NoDEA, 5 (1998), 355-365.
5. T. Cazenave and F. B. Weissler, Scattering theory and self-similar solutions for the nonlinear Schrödinger equation, SIAM J. Math. Anal., 31 (2000), 625-650.
6. M. Escobedo, O. Kavian and H. Matano, Large time behavior of solutions of a dissipative semilinear heat equation, Commun. Partial Differential Equations, 20 (1995), 1427-1452.
7. G. Furioli, On the existence of selfsimilar solutions of the nonlinear Schrödinger equation with power nonlinearity between 1 and 2, Differential and Integral Eqns., to appear.
8. 3) et d'autres espaces fonctionnels limites pour Navier-Stokes, Rev. Mat. Iberoamericana , to appear.
9. V. A. Galaktionov, S. P. Kurdyumov and A. A. Samarskii, On asymptotic "eigenfuctions" of the Cauchy problem for a nonlinear parabolic equation, Math. USSR Sbornik 54 (1986), 421-455.
10. 3 with measures as initial vorticity and Morrey spaces, Commun. Partial Differential Equations, 14 (1989), 577-618.
11. N, J. Differential Equations, 58 (1984), 258-276.
12. L. Herraiz, Asymptotic behavior of solutions of some semilinear parabolic problems, Ann. I. H. P. Anal, non linéaire, 16 (1999), 49-105.
13. S. Kamin and L. A. Peletier, Large time behaviour of solutions of the heat equation with absorption, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 12 (1985), 393-408.
14. O. Kavian, Remarks on the large time behavior of a nonlinear differential equation, Ann. I. H. P. Anal, non linéaire, 4 (1987), 423-452.
15. T. Kawanago, Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity, Ann. I. H. P. Anal. non linéaire, 13 (1996), 1-15.
16. T. Lee and W. Ni, Global existence, large time behavior and life span of solutions of a semilinear parabolic Cauchy problem, Trans. Amer. Math. Soc., 333 (1992), 365-378.
17. Y. Naito and T. Suzuki, Radial symmetry of self-similar solutions for semilinear heat equations, J. Differential Equations, 163 (2000), 407-428.
18. F. Oru, Rôle des oscillations dans quelques problèmes d'analyse non linéaire, Doctoral Thesis, ENS Cachan, 1998.
19. H. Pecher, Self-similar and asymptotically self-similar solutions of nonlinear wave equations, Math. Ann. 316 (2000), 259-281.
20. F. Planchon, Solutions auto-similaires et espaces de données initiales pour l'équation de Schrödinger, C. R. Acad. Sci. Paris, Série I, t. 328 (1999), 1157-1162.
21. n, Rev. Mat. Iberoamericana, 14 (1998), 71-93.
22. n) spaces, Rev. Mat. Iberoamericana, 14 (1998), 1-46.
23. F. Ribaud and A. Youssfi, Regular and self-similar solutions of nonlinear Schrödinger equations, J. Math. Pures Appl., 77 (1998), 1065-1079.
24. F. Ribaud and A. Youssfi, Global solutions and self-similar solutions of semilinear wave equations, Math. Z., to appear.
25. S. Snoussi and S. Tayachi, Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems, Nonlinear Anal., to appear.
26. S. Snoussi and S. Tayachi, Asymptotic self-similar behavior of solutions for a seminlinear parabolic system, Commun. Contemp. Math., to appear
27. S. Snoussi, S. Tayachi and F. B. Weissler, Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term, Proc. Royal Soc. Edinburgh Sect. A., 129 (1999), 1291-1307.
28. C. E. Wayne, Invariant manifolds for parabolic partial differential equations on unbounded domains, Arch. Rational Mech. Anal. 138 (1997), 279-306.
29. F. B. Weissler, Asymptotically self-similar solutions of the two-power nonlinear Schrödinger equation, Adv. Diff. Eqns. 6 (2001), 419-440.