Asymptotics for fractional nonlinear heat equations

Journal of the London Mathematical Society

Volumn 72, Issue 3, 2005, Pages 663-688

  Hayashi, Nakao ^a   Kaikina, Elena I ^b   Naumkin, Pavel I ^c  

^a OSAKA UNIVERSITY   (Japan)

^b INSTITUTO TECNOLÓGICO DE MORELIA   (Mexico)

^c INSTITUTO DE MATEMÁTICAS   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144528081     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/S0024610705006782     Document Type: Article

References (25)

1. C. BARDOS, P. PENEL, U. FRISCH and P. L. SULEM, 'Modified dissipativity for a nonlinear evolution equation arising in turbulence', Arch. Rational Mech. Anal. 71 (1979) 237-256.
2. P. BILER, T. FUNAKI and W. A. WOYCZYNSKI, 'Fractal Burgers equations', J. Differential Equations 148 (1998) 9-46.
3. A. CONSTANTIN and J. ESCHER, 'Wave breaking for nonlinear nonlocal shallow water equations', Acta Math. 181 (1998) 229-243.
4. A. ERDÉLYI, W. MAGNUS, F. OBERHETTINGER and F. G. TRICOMI, Tables of integral transforms, based, in part, on notes left by Harry Bateman (McGraw-Hill, New York, 1954).
5. M. ESCOBEDO and O. KAVIAN, 'Asymptotic behavior of positive solutions of a non-linear heat equation', Houston J. Math. 13 (1987) 39-50.
6. M. ESCOBEDO, O. KAVIAN and H. MATANO, 'Large time behavior of solutions of a dissipative nonlinear heat equation', Comm. Partial Differential Equations 20 (1995) 1427-1452.
7. 1+α, J. Fac. Sci. Univ. Tokyo, Sect. I 13 (1966) 109-124.
8. V. A. GALAKTIONOV, S. P. KURDYUMOV and A. A. SAMARSKII, 'On asymptotic eigenfunctions of the Cauchy problem for a nonlinear parabolic equation', Math. USSR Sb. 54 (1986) 421-455.
9. N, J. Differential Equations 53 (1984) 258-276.
10. K. HAYAKAWA, 'On non-existence of global solutions of some semi-linear parabolic equations', Proc. Japan Acad. 49 (1973) 503-505.
11. N. HAYASHI, N. ITO, E. I. KAIKINA and P. I. NAUMKIN, 'On some nonlinear dissipative equations with sub-critical nonlinearities', Taiwanese J. Math. 8 (2004) 135-154.
12. N. HAYASHI, E. I. KAIKINA and P. I. NAUMKIN, 'Large time behavior of solutions to the dissipative nonlinear Schrödinger equation', Proc. Roy. Soc. Edinburgh 130A (2000) 1029-1043.
13. N. HAYASHI, E. I. KAIKINA and P. I. NAUMKIN, 'Large time behavior of solutions to the Landau-Ginzburg type equation', Funkcial. Ekvac. 44 (2001) 171-200.
14. N. HAYASHI, E. I. KAIKINA and P. I. NAUMKIN, 'Global existence and time decay of small solutions to the Landau-Ginzburg type equations', J. Anal., Math. 90 (2003) 141-173.
15. N. HAYASHI, E. I. KAIKINA and P. I. NAUMKIN, 'Landau-Ginzburg type equations in the sub-critical case', Comm. Contemporary Math. 5 (2003) 127-145.
16. S. KAMIN and L. A. PELETIER., 'Large time behaviour of solutions of the heat equation with absorption', Ann. Scuola Norm. Sup. Pisa 12 (1985) 393-408.
17. O. KAVIAN, 'Remarks on the large time behavior of a nonlinear diffusion equation', Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987) 423-452.
18. K. KOBAYASHl, T. SIRAO and H. TANAKA, 'On the growing up problem for semi-linear heat equations', J. Math. Soc. Japan 29 (1977) 407-424.
19. T. KOMATSU, 'On the martingale problem for generators of stable processes with perturbations', Osaka J. Math. 21 (1984) 113-132.
20. P. I. NAUMKIN and I. A. SHISHMAREV, Nonlinear nonlocal equations in the theory of waves, Translations of Mathematical Monographs 133 (American Mathematical Society, Providence, RI, 1994).
21. M. F. SHLESINGER, G. M. ZASLAVSKY and U. FRISCH (eds) Lévy Sights and related topics in physics, Lecture Notes in Physics 450 (Springer, Berlin, 1995).
22. E. M. STEIN, Singular' integrals and differentiability properties of functions (Princeton University Press, Princeton, NJ, 1970).
23. S. SUGITANI, 'On nonexistence of global solutions for some nonlinear integral equations', Osaka J. Math. 12 (1975) 45-51.
24. M. TAYLOR, 'Analysis on Morrey spaces and application to Navier-Stokes and other evolution equations', Comm. Partial Differential Equations 17 (1992) 1407-1456.
25. F. B. WEISSLER, 'Existence and non-existence of global solutions to a nonlinear heat equation', Israel J. Math. 38 (1988) 29-40.