×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. G. Aronson and H. F. Weinberger,Multidimensional nonlinear diffusion arising in population genetics, Advances in Math.30 (1978), 33–76. · Zbl 0407.92014 · doi:10.1016/0001-8708(78)90130-5
[2] H. Fujita, On the blowing up of solutions of the Cauchy problem for u1 = +u 1+a, J. Fac. Sci. Univ. Tokyo, Sect. I13 (1966), 109–124. · Zbl 0163.34002
[3] H. Fujita,On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., Vol. 18, Part I, Amer. Math. Soc., 1968, pp. 138–161.
[4] A. Haraux and F. B. Weissler,Non-uniqueness for a semilinear initial value problem, preprint. · Zbl 0465.35049
[5] K. Hayakawa,On nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad.49 (1973), 503–505. · Zbl 0281.35039 · doi:10.3792/pja/1195519254
[6] K. Kobayashi, T. Sino and H. Tanaka,On the growing up problem for semilinear heat equations, J. Math. Soc. Japan29 (1977), 407–424. · Zbl 0353.35057 · doi:10.2969/jmsj/02930407
[7] E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N. J., 1971.
[8] F. B. Weissler,Semilinear evolution equations in Banach spaces, J. Functional Analysis32 (1979), 277–296. · Zbl 0419.47031 · doi:10.1016/0022-1236(79)90040-5
[9] F. B. Weissler,Local existence and nonexistence for semilinear parabolic equations in L p, Indiana Univ. Math. J.29 (1980), 79–102. · Zbl 0443.35034 · doi:10.1512/iumj.1980.29.29007
[10] K. Yosida,Functional Analysis, Springer-Verlag, New York, 1971. · Zbl 0217.16001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.