Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type

Tomoyasu Nakagawa; Teruo Ushijima

Publications mathématiques et informatique de Rennes (1976)

  • Issue: S5, page 1-24

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Nakagawa, Tomoyasu, and Ushijima, Teruo. "Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type." Publications mathématiques et informatique de Rennes (1976): 1-24. <http://eudml.org/doc/273785>.

@article{Nakagawa1976,
author = {Nakagawa, Tomoyasu, Ushijima, Teruo},
journal = {Publications mathématiques et informatique de Rennes},
language = {eng},
number = {S5},
pages = {1-24},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type},
url = {http://eudml.org/doc/273785},
year = {1976},
}

TY - JOUR
AU - Nakagawa, Tomoyasu
AU - Ushijima, Teruo
TI - Numerical Analysis of the Semi-Linear Heat Equation of Blow-up Type
JO - Publications mathématiques et informatique de Rennes
PY - 1976
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - S5
SP - 1
EP - 24
LA - eng
UR - http://eudml.org/doc/273785
ER -

References

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  1. [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). Zbl0251.65069MR375802
  2. [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). Zbl0373.65047
  3. [3] Fujita, H., On the blowing up of solutions to the Cauchy problem for u t = Δ u + u 1 + α , J. Fac. Sci. Univ.Tokyo, 13, 109-124 (1966). Zbl0163.34002MR214914
  4. [4] Fujita, H., On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symposium in Pure Math., AMS, 18, 105-113. (1970). Zbl0228.35048MR269995
  5. [5] Ito, S., On the blowing up of solutions for semi-linear parabolic equations (in Japanese), Sugaku, 18, 44-47 (1966). MR219902
  6. [6] Kaplan, S., On the growth of solutions of quasilinear parabolic equations, Comm. Pure Appl. Math., 16, 305-330 (1963). Zbl0156.33503MR160044
  7. [7] Nakagawa, T., Blowing up of a finite difference solution to u t = u χ χ + u 2 , 1974-annual report of the trial research in large scale computation supported by Japanese Ministry of Education, 47-58 (1975). Zbl0357.65075MR423823
  8. [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. [9] Tsutsumi, M., Existence and nonexistence of global solutions for nonlinear parabolic equations, Publ. RIMS, Kyoto Univ., 8, 211-229 (1972). Zbl0248.35074MR312079
  10. [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). Zbl0308.35063MR344679
  11. [11] Ushijima, T., On the finite element approximation of semi-linear parabolic equations (pre-print). 

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