On the growing up problem for semilinear heat equations

Kusuo KOBAYASHI; Tunekiti SIRAO; Hiroshi TANAKA

doi:10.2969/jmsj/02930407

Kusuo KOBAYASHI, Tunekiti SIRAO, Hiroshi TANAKA

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JOURNAL FREE ACCESS

1977 Volume 29 Issue 3 Pages 407-424

DOI https://doi.org/10.2969/jmsj/02930407

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Published: 1977 Received: January 17, 1976 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Hiroshi TANAKA⁴⁾, Kusuo KOBAYASHI¹⁾²⁾, Tunekiti SIRAO³⁾
Right : Kusuo KOBAYASHI¹⁾²⁾, Tunekiti SIRAO³⁾, Hiroshi TANAKA⁴⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Mathematics Hiroshima University
2) Department of Mathematics Japan Toyama University
3) Department of Mathematics Faculty of Science Tokyo Metropolitan University
4) Department of Mathematics Faculty of Science Hiroshima University

Right :
1) Department of Mathematics Hiroshima University
2) Department of Mathematics Toyama University
3) Department of Mathematics Faculty of Science Tokyo Metropolitan University
4) Department of Mathematics Faculty of Science Hiroshima University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Fujita, On the blowing up of solutions of the Cauchy problem for u_t=Δu+u¹+α, J. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124.
2) H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., AMS, 18 (1969), 105-113.
3) K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic differential equations, Proc. Japan Acad., 49 (1973), 503-505.
4) K. Hayakawa, On the limit state of solutions of some semilinear diffusion equations, Osaka J. Math., 12 (1975), 767-776.
5) Y. Kametaka, On nonlinear diffusion equations, Sugaku, 26 (1974), 137-148. (In Japanese.)
6) Ya. I. Kanel', On the stability of the solutions of the equations of combustion theory with finite initial functions, Mat. Sb., 65 (1964), 398-413. (In Russian.)
7) A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un probleme biologique, Bull. Moskov Gos. Univ., Sect. A, 1 (1937), 1-25.
8) K. Masuda, On the growth of solutions of nonlinear diffusion equation u_t=Δu+F(u), Publ. RIMS, Kyoto Univ., 9 (1974), 675-682.
9) S. Sugitani, On nonexistence of global solutions for some nonlinear integral equations, Osaka J. Math., 12 (1975), 45-51.

Right : [1] H. Fujita, On the blowing up of solutions of the Cauchy problem for u_t=Δu+u¹+α, J. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124.
[2] H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., AMS, 18 (1969), 105-113.
[3] K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic differential equations, Proc. Japan Acad., 49 (1973), 503-505.
[4] K. Hayakawa, On the limit state of solutions of some semilinear diffusion equations, Osaka J. Math., 12 (1975), 767-776.
[5] Y. Kametaka, On nonlinear diffusion equations, Sugaku, 26 (1974), 137-148. (In Japanese.)
[6] Ya. I. Kanel', On the stability of the solutions of the equations of combustion theory with finite initial functions, Mat. Sb., 65 (1964), 398-413. (In Russian.)
[7] A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Moskov Gos. Univ., Sect. A, 1 (1937), 1-25.
[8] K. Masuda, On the growth of solutions of nonlinear diffusion equation u_t=Δu+F(u), Publ. RIMS, Kyoto Univ., 9 (1974), 675-682.
[9] S. Sugitani, On nonexistence of global solutions for some nonlinear integral equations, Osaka J. Math., 12 (1975), 45-51.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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