Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity

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1. [CL] T. Cazenave and P.L. Lions, Solutions globales d'équations de la chaleur semi linéaires, Comm. Partial Differ. Equations, Vol. 9, 1984, pp. 955-978. Zbl0555.35067MR755928
2. [D] E. Dibenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J., Vol. 32, 1983, pp. 83-118. Zbl0526.35042MR684758
3. [EZ] Escobedo and Zuazua, Lare time behavior for convection - diffusion equations in RN, J. Func. Anal., Vol. 100, 1991, pp. 119-161. Zbl0762.35011MR1124296
4. [F] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. 1, Vol. 13, 1966, pp. 109-124. Zbl0163.34002MR214914
5. [G] Y. Giga, A bound for global solutions of semilinear heat equations, Comm. Math. Phys., Vol. 103, 1986, pp. 415-421. Zbl0595.35057MR832917
6. [GS] B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. P. D. E., Vol. 6, 1981, pp. 883-901. Zbl0462.35041MR619749
7. [HW] A. Haraux and F.B. Weissler, Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., Vol. 31, 1982, pp. 167-189. Zbl0465.35049MR648169
8. [Kavi] O. Kavian, Remarks on the large time behavior of a nonlinear diffusion equation, Annal. Institut Henri Poincaré - Analyse non linéaire, Vol. 4, 1987, pp. 423-452. Zbl0653.35036MR921547
9. [Kawa] T. Kawanago, Existence and behavior of solutions for ut = Δ(um) + ul, Preprint. MR1454672
10. [Le] H.A. Levine, The role of critical exponents in blowup theorems, SIAM Review, Vol. 32, 1990, pp. 262-288. Zbl0706.35008MR1056055
11. [Li] P.L. Lions, Asymptotic behavior of some nonlinear heat equations, Physica 5D, 1982, pp. 293-306. Zbl1194.35459MR680566
12. [LN] T.Y. Lee and W.M. Ni, Global existence, large time behavior and life span of solutions of semilinear parabolic Cauchy problem, Trans. Amer. Math. Soc., Vol. 333, 1992, pp. 365-371. Zbl0785.35011MR1057781
13. [NST] W.M. Ni, P.E. Sacks and J. Tavatzis, On the asymptotic behavior of solutions of certain quasilinear equation of parabolic type, J. Differ. Equations, Vol. 54, 1984, pp. 97-120. Zbl0565.35053MR756548
14. [S] P.E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal., Vol. 7, 1983, pp. 387-404. Zbl0511.35052MR696738
15. [Si] L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problem, Annals Math., Vol. 118, 1983, pp. 525-571. Zbl0549.35071MR727703
16. [W] X. Wang, On the Cauchy problem for reaction - diffusion equations, Trans. Amer. Math. Soc., Vol. 337, 1993, pp. 549-590. Zbl0815.35048MR1153016