Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type
Publications mathématiques et informatique de Rennes no. S5  (1976), article no. 13, 24 p.
@article{PSMIR_1976___S5_A13_0,
     author = {Nakagawa, Tomoyasu and Ushijima, Teruo},
     title = {Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type},
     journal = {Publications math\'ematiques et informatique de Rennes},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S5},
     year = {1976},
     language = {en},
     url = {http://www.numdam.org/item/PSMIR_1976___S5_A13_0}
}
Nakagawa, Tomoyasu; Ushijima, Teruo. Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type. Publications mathématiques et informatique de Rennes, no. S5 (1976), article  no. 13, 24 p. http://www.numdam.org/item/PSMIR_1976___S5_A13_0/

[1] Ciarlet, P. G. and P. A. Raviart, Maximum principle and uniform convergence for the finite element method, Computer methods in applied mechanics and engineering, 2, 17-31 (1973). | MR 375802 | Zbl 0251.65069

[2] Fujii, H., Some remarks on finite element analysis of time-dependent field problems, Theory and practice in finite element structural analysis, (Tokyo Univ. Press, Tokyo, 1973). | Zbl 0373.65047

[3] Fujita, H., On the blowing up of solutions to the Cauchy problem for u t =Δu+u 1+α , J. Fac. Sci. Univ. Tokyo, 13, 109-124 (1966). | MR 214914 | Zbl 0163.34002

[4] Fujita, H., On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symposium in Pure Math., AMS, 18, 105-113. (1970). | MR 269995 | Zbl 0228.35048

[5] Ito, S., On the blowing up of solutions for semi-linear parabolic equations (in Japanese), Sugaku, 18, 44-47 (1966). | MR 219902

[6] Kaplan, S., On the growth of solutions of quasilinear parabolic equations, Comm. Pure Appl. Math., 16, 305-330 (1963). | MR 160044 | Zbl 0156.33503

[7] Nakagawa, T., Blowing up of a finite difference solution to u t =u χχ +u 2 , 1974-annual report of the trial research in large scale computation supported by Japanese Ministry of Education, 47-58 (1975). | MR 423823 | Zbl 0357.65075

[8] Nakagawa, T. and T. Ushijima, On numerical analysis of the semi-linear heat equation of blow-up type, Symposium on evolution systems and free boundary problems held at RIMS, Kyoto Univ. in Nov. 1975.

[9] Tsutsumi, M., Existence and nonexistence of global solutions for nonlinear parabolic equations, Publ. RIMS, Kyoto Univ., 8, 211-229 (1972). | MR 312079 | Zbl 0248.35074

[10] Tsutsumi, M., Existence and nonexistence of global solutions of the first boundary value problem for a certain quasilinear parabolic equation, Funkcialaj Ekvacioj, 17, 13-24 (1974). | MR 344679 | Zbl 0308.35063

[11] Ushijima, T., On the finite element approximation of semi-linear parabolic equations (pre-print).