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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1969-0239379-X
MathSciNet review: 0239379
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  • [1] E. B. Dynkin, Markov processes, Springer, New York, 1965.
  • [2] H. Fujita, On the blowing up of solutions of the Cauchy problem for $ {u_t} = \Delta u + {u^{1 + \alpha }}$, J. Fac. Sci. Univ. Tokyo 13 (1966), 109-124. MR 0214914 (35:5761)
  • [3] N. Ikeda, M. Nagasawa and S. Watanabe, Branching Markov processes, J. Math. Kyoto Univ. 8 (1968). Abstracts, Proc. Japan Acad. 41 (1965), 816-821 ; 42 (1966), 252-257, 370-375, 380-384, 719-724, 1016-1021, 1022-1026. MR 0202195 (34:2068)
  • [4] -, Foundation of branching Markov processes, Seminar on Probability Vol. 23, 1966. (Japanese)
  • [5] K. Ito and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer, New York, 1965. MR 0199891 (33:8031)
  • [6] S. Ito, On the blowing up of solutions of semi-linear parabolic equations. Bull. Math. Soc. Japan (Sûgaku) 18 (1966) 44-47. (Japanese) MR 0219902 (36:2973)
  • [7] M. Nagasawa, On construction of branching Markov process with age and sign, Kōdai Math. Sem. Rep. 20 (1968), 469-508. MR 0247677 (40:940)
  • [8] T. Sirao, On signed branching Markov processes with age, Nagoya Math. J. 32 (1968), 155-225. MR 0232443 (38:768)

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

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