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Existence and non-existence of global solutions for a semilinear heat equation. (English) Zbl 0476.35043


MSC:

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35B35 Stability in context of PDEs
35K05 Heat equation
35B60 Continuation and prolongation of solutions to PDEs
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[2] Fujita, H., On the blowing up of solutions of the Cauchy problem for u_1 = ▽u +u^1+a, J. Fac. Sci. Univ. Tokyo, Sect. I, 13, 109-124 (1966) · Zbl 0163.34002
[3] Fujita, H., On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., 18, 138-161 (1968) · Zbl 0228.35048
[4] A. Haraux and F. B. Weissler,Non-uniqueness for a semilinear initial value problem, preprint. · Zbl 0465.35049
[5] Hayakawa, K., On nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49, 503-505 (1973) · Zbl 0281.35039 · doi:10.3792/pja/1195519254
[6] Kobayashi, K.; Sino, T.; Tanaka, H., On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, 29, 407-424 (1977) · Zbl 0353.35057
[7] Stein, E. M., Singular Integrals and Differentiability Properties of Functions (1971), Princeton, N. J.: Princeton University Press, Princeton, N. J.
[8] Weissler, F. B., Semilinear evolution equations in Banach spaces, J. Functional Analysis, 32, 277-296 (1979) · Zbl 0419.47031 · doi:10.1016/0022-1236(79)90040-5
[9] Weissler, F. B., Local existence and nonexistence for semilinear parabolic equations in L^p, Indiana Univ. Math. J., 29, 79-102 (1980) · Zbl 0443.35034 · doi:10.1512/iumj.1980.29.29007
[10] Yosida, K., Functional Analysis (1971), New York: Springer-Verlag, New York · Zbl 0217.16001
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