Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Probabilistic treatment of the blowing up of solutions for a nonlinear integral equation


Authors: Masao Nagasawa and Tunekiti Sirao
Journal: Trans. Amer. Math. Soc. 139 (1969), 301-310
MSC: Primary 45.30; Secondary 35.00
MathSciNet review: 0239379
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  • [1] E. B. Dynkin, Markov processes, Springer, New York, 1965.
  • [2] Hiroshi Fujita, On the blowing up of solutions of the Cauchy problem for 𝑢_{𝑡}=Δ𝑢+𝑢^{1+𝛼}, J. Fac. Sci. Univ. Tokyo Sect. I 13 (1966), 109–124 (1966). MR 0214914
  • [3] Nobuyuki Ikeda, Masao Nagasawa, and Shinzo Watanabe, On branching Markov processes, Proc. Japan Acad. 41 (1965), 816–821. MR 0202195
  • [4] -, Foundation of branching Markov processes, Seminar on Probability Vol. 23, 1966. (Japanese)
  • [5] Kiyoshi Itô and Henry P. McKean Jr., Diffusion processes and their sample paths, Die Grundlehren der Mathematischen Wissenschaften, Band 125, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-New York, 1965. MR 0199891
  • [6] Seizô Itô, On blowing up of solutions of semilinear partial differential equations of parabolic type, Sûgaku 18 (1966), 44–47 (Japanese). MR 0219902
  • [7] Masao Nagasawa, Construction of branching Markov processes with age and sign, Kōdai Math. Sem. Rep. 20 (1968), 469–508. MR 0247677
  • [8] Tunekiti Sirao, On signed branching Markov processes with age, Nagoya Math. J. 32 (1968), 155–225. MR 0232443

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DOI: http://dx.doi.org/10.1090/S0002-9947-1969-0239379-X
Article copyright: © Copyright 1969 American Mathematical Society