Quelques propriétés de solutions d'équations et d'inéquations d'évolution paraboliques non linéaires

 Access to full text

 Full (PDF)

1. S. Agmon - L. Nirenberg: [1] Properties of solutions of ordinary differential equations in Banach spaces, Comm. Pure Appl. Math., 16 (1963), pp. 121-239. Zbl0117.10001MR155203
2. L. Amerio - G. Prouse: [1] Abstract almost periodic functions and functional analysis, Van Nostrand, New York (1970) . 
3. C. Bardos - L. Tartar: [1] Sur l'unicité rétrograde des équations d'évolution, C. R. Acad. Sc. Paris, 273 (1971), pp. 1239-1241. [2] About backward uniqueness for evolution equations and some related questions. Zbl0232.47018MR290186
4. M. Biroli: [1] Solutions presque périodiques des inéquations d'évolution paraboliques, Ann. Mat. Pura Appl., 88 (1971), pp. 51-70. Zbl0221.35037MR326492
5. F.E. Browder: [1] Existence of periodic solutions for nonlinear parabolic equations of evolution, Proc. Nat. Acad. Sc., 53 (1965), pp. 1100-1103. Zbl0135.17601MR177295
6. [2] Periodic solution of nonlinear equation of evolution in infinite dimensional spaces, Lecture Series in Diff. Equat. Univ. of Maryland (1966). 
7. A. Friedman: [1] Convergence of solutions of parabolic equations to a steady state, J. Math. Mech., 8 (1959), pp. 57-76. Zbl0083.32102MR101963
8. [2] Generalised heat transfer between solids and gases under nonlinear boundary conditions, J. Math. Mech., 82 (1959), pp. 161-183. Zbl0101.31102MR102345
9. [3] Asymptotic behaviour of solutions of parabolic equations, J. Math. Mech., 83 (1959), pp. 387-392. Zbl0088.07502MR101964
10. [4] Asymptotic behaviour of solutions of parabolic equations of any order, Acta Mat., 106 (1961), pp. 1-43. Zbl0102.09001MR136869
11. [5] Remarks on nonlinear parabolic equations, Proc. Sym. Appl. Math., 17 (1965), pp. 3-49. MR186938
12. [6] Partial differential equations, part 2, Holt, Reinehard and Winston Inc. (1969). MR445088
13. H. Fujita: [1] On the blowing up of solutions of the Cauchy problem for ut = Δu + u1+α, J. Fac. Sci. Univ. Tokyo, 13 (1966), pp. 109-124. Zbl0163.34002
14. [2] On the nonlinear equations Δu + eu = 0 and ∂v/∂t = Δv + ev, Bull. Amer. Math. Soc., 75 (1969), pp. 132-135. 
15. S. Itô: [1] On the blowing up of solutions of semilinear parabolic equations, Bull. Math. Soc. Japan (Sûgaku), 181 (1966), pp. 44-47. MR219902
16. S. Kaplan: [1] On the growth of quasilinear parabolic equations, Comm. Pure Appl. Math., 16 (1963), pp. 305-330. Zbl0156.33503MR160044
17. H.A. Levine: [1] Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put = - Au + F(u), Arch. Rational Mech. Anal., 51 (5) (1973), pp. 371-385. Zbl0278.35052MR348216
18. J.L. Lions: [1] Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris (1969). Zbl0189.40603
19. O.A. Oleinik: [1] On the existence, uniqueness, stability and approximation of solutions o f Prandtl's system for the nonstationary boundary layer, Rend. Acc. Naz. Lincei, 41 (1966), pp. 32-40. Zbl0148.22203MR208905
20. M.C. Pellisier - L. Reynaud: [1] Ecoulement d'un glacier de vallée avec une loi de frottement solide, C. R. Acad. Sci. Paris, série A, à paraitre 1974. 
21. G. Prodi: [1] Soluzioni periodiche di equazioni alle derivate parziali di tipo parabolico e non lineari, Riv. Mat. Univ. Parma, 3 (1952), pp. 265-290. Zbl0049.07502MR55543
22. [2] Problemi al contorno non lineari per equazioni di tipo parabolico non lineari in due variabili-soluzioni periodiche, Rend. Sem. Mat. Padova, 23 (1954), pp. 25-85. Zbl0055.32701MR60704
23. G. Prouse: [1] Periodic or almost periodic solutions of a nonlinear functional equation, Rend. Acc. Naz. Lincei, 43 (1967), pp. 161-167, 281-287, 448-452; 44 (1968), pp. 3-10. Zbl0159.20101
24. J.-P. Puel: [1] Existence, comportement à l'infini et stabilité dans certains problèmes quasi linéaires elliptiques et paraboliques d'ordre 2, Univ. Paris VI, Analyse Numérique L.A., 189 Place Jussieu, Paris 5ème, 1974. 
25. D.H. Sattinger: [1] Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J., 212 (1972), pp. 979-1000. Zbl0223.35038MR299921
26. J. Simon: [1] Existence et unicité de solutions d'équations et d'inéquations d'évolution sur )- ∞ + ∞(, C. R. Acad. Sci. Paris, t. 274 (1972), pp. 1045-1047. Zbl0243.35056
27. [2] Une majoration et quelques résultats sur le comportement à l'infini de solutions d'équations fortement non linéaires, C. R. Acad. Sci. Paris, t. 279 (1974), pp. 421-424. Zbl0299.65051MR437935
28. L. Tartar: [1] Communication personnelle. 

1. Maria Giovanna Garroni, Maria Agostina Vivaldi, Régularité de la solution forte de problèmes non linéaires d'évolution