Remarks on the large time behaviour of a nonlinear diffusion equation

Otared Kavian

Annales de l'I.H.P. Analyse non linéaire (1987)

  • Volume: 4, Issue: 5, page 423-452
  • ISSN: 0294-1449

How to cite

top

Kavian, Otared. "Remarks on the large time behaviour of a nonlinear diffusion equation." Annales de l'I.H.P. Analyse non linéaire 4.5 (1987): 423-452. <http://eudml.org/doc/78139>.

@article{Kavian1987,
author = {Kavian, Otared},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {diffusion; blows-up in finite time; global existence; blow-up},
language = {eng},
number = {5},
pages = {423-452},
publisher = {Gauthier-Villars},
title = {Remarks on the large time behaviour of a nonlinear diffusion equation},
url = {http://eudml.org/doc/78139},
volume = {4},
year = {1987},
}

TY - JOUR
AU - Kavian, Otared
TI - Remarks on the large time behaviour of a nonlinear diffusion equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 5
SP - 423
EP - 452
LA - eng
KW - diffusion; blows-up in finite time; global existence; blow-up
UR - http://eudml.org/doc/78139
ER -

References

top
  1. [1] D.G. Aronson and H.F. Weingerger, Muldimensional Nonlinear Diffusion Arising in Population genetics, Advances in Math., Vol. 30, 1978, pp. 33-76. Zbl0407.92014MR511740
  2. [2] Th. Cazenave and P.L. Lions, Solutions globales de l'équation de la chaleur semi-linéaires, Comm. in P.D.E. Vol. 9, (10), 1984, pp. 955-978. Zbl0555.35067MR755928
  3. [3] M. Escobedo and O. Kavian, Variational Problems Related to Self-Similar Solutions of the Heat equation, J. of Nonlinear Analysis, Theory, Methods and Appl. (to appear). Zbl0639.35038MR913672
  4. [4] M. Escobedo and O. Kavian, Asymptotic Behaviour of Positive Solutions of a Non-linear Heat Equation (to appear). Zbl0666.35046
  5. [5] M. Escobedo, O. Kavian and H. Matano, in preparation. 
  6. [6] H. Fujita, On the Blowing-Up of Solutions of the Cauchy Problem for ut=Δu+u1+α, J. Fac. Sci. Univ. of Tokyo, Sect I, Vol. 13, 1966, pp. 109-124. Zbl0163.34002MR214914
  7. [7] Y. Giga, A Remark on a priori Bounds for Global Solutions of a Semi-Linear Heat Equation, Preprint. 
  8. [8] A. Haraux and F.B. WeisslerNon-Uniqueness for a Semi-Linear Initial Value Problem, Indiana Univ. Math. J., vol 31, n° 2, 1982, pp. 167-189. Zbl0465.35049MR648169
  9. [9] K. Hayakawa, On Non-Existence of Global Solutions of Some Semi-Linear Parabolic Equations, Proc. Japan Acad., Vol. 49, 1973, pp. 503-505. Zbl0281.35039MR338569
  10. [10] K. Kobayashi, T. Sirao et H. Tanaka, On the Growing up Problem for Semi-Linear Heat Equations, J. Math. Soc. Japan, Vol. 29, 1977, pp. 407-424. Zbl0353.35057MR450783
  11. [11] L.E. Payne and D.H. Sattinger, Saddle Points and Instability of Non-linear Hyperbolic Equations, Israël J. of Math., vol. 22, n° 3–4, 1975, pp. 273-303. Zbl0317.35059MR402291
  12. [12] D.H. Sattinger, On Global Solution of Nonlinear Hyperbolic Equations, Arch. Rat. Mech. and Analysis, Vol. 30, 1968, pp. 148-172. Zbl0159.39102MR227616
  13. [13] F.B. Weissler, Existence and Non-Existence of Global Solutions for a Semi-Linear Heat Equation, Israël J. of Math., Vol. 38, n° 1-2, 1981, pp. 29-39. Zbl0476.35043MR599472
  14. [14] F.B. Weissler, Rapidly Decaying Solutions of an O.D.E. with Application to Semi-linear Parabolic P.D.E.'s. (to appear). 
  15. [15] C.M. Dafermos, Asymptotic Behavior of Solutions of Evolution Equations in Non-linear Evolution Equations, M. G. CRANDALL Ed., pp. 103-123, Academic Press, New York, 1978. Zbl0499.35015MR513814

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.