A blow-up result for nonlinear diffusion equations

Marek Fila; Ján Filo

Mathematica Slovaca (1989)

  • Volume: 39, Issue: 3, page 331-346
  • ISSN: 0232-0525

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Fila, Marek, and Filo, Ján. "A blow-up result for nonlinear diffusion equations." Mathematica Slovaca 39.3 (1989): 331-346. <http://eudml.org/doc/32240>.

@article{Fila1989,
author = {Fila, Marek, Filo, Ján},
journal = {Mathematica Slovaca},
keywords = {blow-up; nonlinear diffusion; nonexistence of global solutions; initial boundary value},
language = {eng},
number = {3},
pages = {331-346},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A blow-up result for nonlinear diffusion equations},
url = {http://eudml.org/doc/32240},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Fila, Marek
AU - Filo, Ján
TI - A blow-up result for nonlinear diffusion equations
JO - Mathematica Slovaca
PY - 1989
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 39
IS - 3
SP - 331
EP - 346
LA - eng
KW - blow-up; nonlinear diffusion; nonexistence of global solutions; initial boundary value
UR - http://eudml.org/doc/32240
ER -

References

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  2. BALL J. M., Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford, (2), 28, 1977, 473-486. (1977) Zbl0377.35037MR0473484
  3. BERGER M. S., Nonlinearity and functional analysis, Academic Press 1977. (1977) Zbl0368.47001MR0488101
  4. FILA M., FILO J., Stabilization of solutions of certain one-dimensional degentrate diffusion equations, Math. Slovaca 37, 1987, 217-229. (1987) MR0899439
  5. FILO J., On solutions of a pertuгbed fast diffusion equation, Aplikace matematiky 32, 1987, 364-380. (1987) MR0909544
  6. FRIEDMAN A., Partial differential equations of parabolic type, Prentice-Hall, N.J. 1964. (1964) Zbl0144.34903MR0181836
  7. FRIEDMAN A., Partial differential equations, Holt, Rinehart and Winston, New York 1969. (1969) Zbl0224.35002MR0445088
  8. FUJITA H., On the blowing up of solutions of the Cauchy problem for u t = u + u 1 + a . , J. Fac. Sci. Univ. Tokyo, Sect. 1A 13, 1966, 109-124. (1966) MR0214914
  9. GALAKTIONOV V. A., A boundary value problem for the nonlinear parabolic equation u t = u 1 + α + u β , Differential equations 17, 1981, 551-555 (Russian). (1981) MR0616920
  10. LADYZENSKAJA O. A., SOLONNIKOV V. A., URALCEVA N. N., Lineaг and quasilinear equations of paгabolic type, Nauka, Moscow 1967. (1967) 
  11. LEVINE H. A., SACKS P. E., Some existence and nonexistence theorems for solutions of degenerate parabolic equations, J. Differential Equations 52, 1984, 135-161. (1984) Zbl0487.34003MR0741265
  12. NAKAO M., Existence, nonexistence and some asymptotic behaviour of global solutions of a nonlinear degenerate parabolic equation, Math. Rep. College of Gen. Edc, Kyushu Univ. 14, 1983, 1-21. (1983) Zbl0563.35038MR0737351
  13. NAKAO M., Lp-estimates of solution of some nonlinear degenerate diffusion equations, J. Math. Soc. Japan 37, 1985, 41-63. (1985) MR0769776
  14. SACKS P. E., Continuity of solutions of a singular parabolic equation, Nonlinear Analysis 7, 1983, 387-409. (1983) Zbl0511.35052MR0696738
  15. SATTINGER D. H., PAYNE L. E., Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22, 1975, 273-303. (1975) MR0402291
  16. TSUTSUMI M., Existence and nonexistence of global solutions for nonlinear parabolic equations, Publ. R.I.M.S., Kyoto Univ. 8, 1972/73, 211-229. (1972) Zbl0248.35074MR0312079

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