Estimations C1 pour des problèmes paraboliques semi-linéaires

A. Haraux; M. Kirane

Annales de la Faculté des sciences de Toulouse : Mathématiques (1983)

  • Volume: 5, Issue: 3-4, page 265-280
  • ISSN: 0240-2963

How to cite


Haraux, A., and Kirane, M.. "Estimations C1 pour des problèmes paraboliques semi-linéaires." Annales de la Faculté des sciences de Toulouse : Mathématiques 5.3-4 (1983): 265-280. <>.

author = {Haraux, A., Kirane, M.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {semi-linear initial value problems; smoothing effect; positive solutions},
language = {fre},
number = {3-4},
pages = {265-280},
title = {Estimations C1 pour des problèmes paraboliques semi-linéaires},
url = {},
volume = {5},
year = {1983},

AU - Haraux, A.
AU - Kirane, M.
TI - Estimations C1 pour des problèmes paraboliques semi-linéaires
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1983
VL - 5
IS - 3-4
SP - 265
EP - 280
LA - fre
KW - semi-linear initial value problems; smoothing effect; positive solutions
UR -
ER -


  1. [1] S. Agmon. «On the eigenfunctions and on the eigenvalues of general boundary value problems». Comm. Pure Appl. Math.15 (1962),116-147. Zbl0109.32701MR147774
  2. [2] N.D. Alikakos. «Lp bounds of solutions of reaction - diffusion equations». Comm. P. Diff. Eq.4 (1979), 827-868. Zbl0421.35009MR537465
  3. [3] H. Brezis. «Propriétés régularisantes de certains semi-groupes non linéaires». Israël J. Math.9 (1971 ), 513-534. Zbl0213.14903MR283635
  4. [4] H. Brezis. Cours de 3ème cycle Paris VI (1977). 
  5. [5] H. Brezis et J.A. Goldstein. «Liouville theorems for some improperly posed problems». Dans Improperly posed boundary value problems. Carasso-Stone ed., Pitman (1975), 65-75. Zbl0318.35072MR477353
  6. [6] M.G. Crandall, A. Pazy et L. Tartar. «Remarks on generators of analytic semi-groups». Israël J. Math.32, 4 (1979), 363-374. Zbl0436.47028MR571090
  7. [7] C.M. Dafermos. «Asymptotic behavior of solutions of evolution equations». dans Nonlinear Evolution Equations, M.G. Crandall ed., Academic Press, New-York (1978) 103-123. Zbl0499.35015MR513814
  8. [8] G. Da Prato et P. Grisvard. «Equations d'évolution abstraites non linéaires de type parabolique». C.R.A.S.Paris t. 283 (1976), 709-711. Zbl0356.35048MR425694
  9. [9] J.P. Dias ET A. Haraux. «Smoothing effect and asymptotic behavior for the solutions of a nonlinear time dependent system». Proc. Roy. Soc. Edinburgh87A (1981), 289-303. Zbl0458.35054MR606337
  10. [10] L.C. Evans. «Application of nonlinear semi-group theory to certain partial differential equations, Nonlinear Evolution Equations , M.G. Crandall ed., Academic Press, New-York (1978). Zbl0471.35039
  11. [11] A. Friedman. «Partial differential equations». Halt, Rinehart and Winston, New-York (1969). Zbl0224.35002MR445088
  12. [12] J.K. Hale. «Ordinary differential equations». Wiley-Interscience, New-York (1969). Zbl0186.40901MR419901
  13. [13] J.K. Hale and P. Massatt. «Asymptotic behavior of gradient-like systems». To appear. Zbl0542.34027MR703689
  14. [14] D. Henry. «Geometric Theory of Semilinear Parabolic Equations». Lecture Notes in Math.. N° 842, Springer (1981 ). Zbl0456.35001MR610244
  15. [15] T. Kato. «Abstract evolution equations of parabolic type in Banach and Hilbert spaces». Nagoya Math. J.19 (1961), 93-125. Zbl0114.06102MR143065
  16. [16] J.P. La Salle. «Stability theory and invariance principles». Dynamical Systems, An International Symposium . ed. L. Cesari, J.K. Hale and J.P. La Salle, Academic Press, New-York (1976), Vol. I, 211-222. Zbl0356.34047MR594977
  17. [17] P.L. Lions. «Structure of the set of steady-state solutions and asymptotic behavior of semilinear heat equations». A paraître. Zbl0491.35057
  18. [18] H. Matano. «Convergence of solutions of one-dimensional semilinear parabolic equations». J. Math. Kyoto Univ., 18 (1978), 221-227. Zbl0387.35008MR501842
  19. [19] A. Pazy. «Semi-groups of operators and applications to partial differential equations». Univ. of Maryland Press (1974). MR512912
  20. [20] I. Segal. «Non-linear semi-groups». Ann. Math.78 (1963), 339-364. Zbl0204.16004MR152908
  21. [21] E.M. Stein. «Topics in harmonic analysis». Annals of Math. Studies, Princeton Univ. Press. Zbl0193.10502MR252961
  22. [22] H.B. Stewart. «Generation of analytic semi-groups by strongly elliptic operators». Trans. Amer. Math. Soc.199 (1974), 141-162. Zbl0264.35043MR358067
  23. [23] G.F. Webb. «A reaction-diffusion model for a deterministic diffusive epidemic». J. of Math. Anal. and Appl.84,1 (1981), 150-161. Zbl0484.92019MR639529
  24. [24] F.B. Weissler. «Semilinear evolution equations in Banach spaces». J. Funct. Anal.32 (1979), 277-296. Zbl0419.47031MR538855

NotesEmbed ?


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.