Hiroshima Mathematical Journal

On some semilinear evolution equations with time-lag

Kusuo Kobayashi

Full-text: Open access

Article information

Hiroshima Math. J., Volume 10, Number 1 (1980), 189-227.

First available in Project Euclid: 21 March 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K22
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]


Kobayashi, Kusuo. On some semilinear evolution equations with time-lag. Hiroshima Math. J. 10 (1980), no. 1, 189--227. doi:10.32917/hmj/1206134584. https://projecteuclid.org/euclid.hmj/1206134584

Export citation


  • [1] D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Advances in Math. 30 (1978), 33-76.
  • [2] S. Bochner, Harmonic analysis and the theory of probability, University of California Press, Berkeley and Los Angeles, 1960.
  • [3] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut = uJ u+a, J. Fac. Sci. Univ. Tokyo Sect. I 13 (1966), 109-124.
  • [4] H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., AMS 18 (1969), 105-113.
  • [5] K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic differential equations, Proc. Japan Acad. 49 (1973), 503-505.
  • [6] K. Hayakawa, On the limit state of solutions of some semilinear diffusion equations, Osaka J. Math. 12 (1975), 767-776.
  • [7] A. Inoue, T. Miyakawa and K. Yoshida, Some properties of solutions for semilinear heat equations with time-lag, J. Differential Equations 24 (1977), 383-396.
  • [8] Y. Karnetaka, On nonlinear diffusion equations, Sugaku 26 (1974), 137-148. (In Japanese.)
  • [9] Ya. I. Kane, On the stability of the solutions of the equations of combustion theory with finite initial functions, Mat. Sb. 65 (1964), 398-413. (In Russian.) [10] K. Kobayashi, On the semilinear heat equations with time-lag, Hiroshima Math. J. 7 (1977), 459-472.
  • [11] K. Kobayashi, T. Sirao and H. Tanaka, On the growing up problem for semilinear heat equations, J. Math. Soc. Japan 29 (1977), 407-424.
  • [12] A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Etude de equation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Bull. Moskov Gos. Univ., Sect. A 1 (1937), 1-25.
  • [13] K. Masuda, On the growth of solutions of nonlinear diffusion equation ut = u+F(u), Publ. Res. Inst. Math. Sci. 9 (1974) 675-682.
  • [14] M. Nagasawa and T. Sirao, Probabilistic treatment of the blowing up of solutions for a nonlinear integral equation, Trans. Amer. Math. Soc. 139 (1969), 301-310.
  • [15] S. Sugitani, On nonexistence of global solutions for some nonlinear integral equations, Osaka J. Math. 12 (1975), 45-51.