Estimations C1 pour des problèmes paraboliques semi-linéaires

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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

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