da Prato, Giuseppe; Grisvard, Pierre Equations d’évolution abstraites non linéaires de type parabolique. (French) Zbl 0471.35036 Ann. Mat. Pura Appl., IV. Ser. 120, 329-396 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 104 Documents MSC: 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 35K55 Nonlinear parabolic equations 34G20 Nonlinear differential equations in abstract spaces Keywords:linearization method; local solution; interpolation spaces PDF BibTeX XML Cite \textit{G. da Prato} and \textit{P. Grisvard}, Ann. Mat. Pura Appl. (4) 120, 329--396 (1979; Zbl 0471.35036) Full Text: DOI References: [1] Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Applied. Math., 15, 119-119 (1962) · Zbl 0109.32701 [2] Agmon; Douglis; Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations, Comm. Pure Applied Math., 12, 623-623 (1959) · Zbl 0093.10401 [3] Benilan-Ha, Equations d’évolution du type (du/dt) + β∂φ(u)∋0 dans L^∞(Ω), Note C.R.A.S., 281, 947-950 (1975) · Zbl 0315.35078 [4] Brezis,Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies 5, North Holland, 1973. · Zbl 0252.47055 [5] Brezis - Fraenkel,A function with prescribed initial derivatives in different Banach spaces (à para’tre). · Zbl 0388.46026 [6] Bruce; Stewart, Generation of analytic semi-groups by strongly elliptic operators, Transactions Amer. Math. Soc., 199, 141-162 (1977) · Zbl 0264.35043 [7] Crandall; Liggett, Generation of nonlinear transformations in general Banach spaces, Amer. J. Math., 93, 265-298 (1971) · Zbl 0226.47038 [8] Crandall; Pazy, Nonlinear evolution equations in B-spaces, Israël J. of Math., 11, 57-94 (1972) · Zbl 0249.34049 [9] Da Prato; Grisvard, Sommes d’opérateurs linéaires et équations différentielles opérationnelles, J. de Maths. pures et appliquées, 54, 305-387 (1975) · Zbl 0315.47009 [10] Da Prato; Grisvard, Equations d’évolution abstraites non linéaires de type parabolique, Note C.R.A.S., 283, 709-711 (1976) · Zbl 0356.35048 [11] Dunford - Schwartz,Linear operators, tomes 1 et 2, Intersciences Publishers, New York. [12] Friedman, Remarks on non linear parabolic equations, Proc. Symp. Appl. Math., 17, 297-350 (1965) [13] Glazman; Lioubitch, Analyse Linéaire en dimension finie (1969), Moscou: Nanka, Moscou [14] Grisvard, Commutativité de deux foncteurs d’interpolation et applications, J. de Maths. pures et appliquées, 45, 143-290 (1966) · Zbl 0173.15803 [15] Grisvard, Equations différentielles abstraites, Ann. Sc. E.N.S., Paris, 2, 311-395 (1969) · Zbl 0193.43502 [16] Kato,Accretive operators and nonlinear evolution equations in B-spaces, Proc. Symp. A.M.S., 1968. [17] Komura, Nonlinear semi-groups in Hilbert spaces, J. Math. Soc. Japan, 19, 493-507 (1967) · Zbl 0163.38302 [18] Lions; Peetre, Sur une classe d’espaces d’interpolation, Publications I.H.E.S. Paris, 19, 5-68 (1963) · Zbl 0148.11403 [19] Mihlin, Sur les multiplicateurs des intégrales de Fourier, Doklady Akad. Nauk. S.S.S.R., 109, 4, 701-703 (1956) [20] Nikolski, Sur les théorèmes d’immersion, de prolongement et d’approximation pour les fonctions différentiable sde plusieurs variables, Uspehi Mat. Nauk., 16, 63-114 (1961) [21] Pazy,Semi-groups of linear operators and applications to partial differential equations, Lecture Notes no. 10, University of Maryland, 1974. [22] Sinestrari - Vernole,Semi linear evolution equations in interpolation space. Non Linear Analysis,1, no. 3 (1977), pp. 249-261. · Zbl 0357.34061 [23] Sobolevski, Equations of parabolic type in a Banach space, Trudy Mockovkogo Mat. Obsch., 10, 297-350 (1961) [24] Stein,Singular integrals and differentiability properties of functions, Princeton University Press, 1970. · Zbl 0207.13501 [25] Zolesio,Multiplications dans les espaces de Besov, Proceedings of the Royal Academy of Scotland. · Zbl 0382.46020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.