References
Acquistapace, P., Terreni, B.: Some existence and regularity results for abstract nonautonomous parabolic equations. J. Math. Anal. Appl. (to appear)
Acquistapace, P., Terreni, B.: On the abstract non autonomous Cauchy problem in the case of constant domains. Ann. Math. Pura Appl. (to appear)
Agmon, S.: On the eigenfunctions and the eigenvalues of general elliptic boundary value problems. Comm. Pure Appl. Math.15, 119–147 (1962)
Browder, F.: On the spectral theory of elliptic differential operators. I. Math. Ann.142, 22–130 (1961)
Campanato, S.: Generation of analytic semigroups by elliptic operators of second order in Hölder spaces. Ann. Scuola Norm. Sup. Pisa (IV)8, 495–512 (1981)
Da Prato, G., Grisvard, P.: Equations d'évolution abstraites non linéaires de type parabolique. Ann. Mat. Pura Appl.120, 329–396 (1979)
Grisvard, P.: Commutativité de deux foncteurs d'interpolation et applications. J. Math. Pures Appl.45, 143–290 (1966)
Friedman, A.: Partial differential equations. New York, Toronto: Holt, Rinehart & Winston 1969
Kato, T.: Perturbation theory. 2nd Edit. Berlin, Heidelberg, New York: Springer 1966
Ladyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and quasilinear equations of parabolic type. Mathematical Monographs, Amer. Math. Soc. Transl. (1968)
Lions, J.L.: Théorèmes de trace et d'interpolation. I. Ann. Scuola Norm. Sup. Pisa13, 389–403 (1959)
Lunardi, A.: Analyticity of the maximal solution of an abstract nonlinear parabolic equation. Nonl. An.5, 503–521 (1982)
Lunardi, A.: Interpolation spaces between domains of elliptic operators and spaces of continuous function with applications to nonlinear parabolic equations. Math. Nachtr. (to appear)
Lunardi, A.: Global solutions of quasilinear abstract parabolic equations. J. Differential Equations (to appear)
Mlak, W.: An example of the equationu t =u xx *f(t, x, u) with distinct maximum and minimum solutions of a mixed problem. Ann. Polon. Math.13, 101–103 (1963)
Poitier-Ferry, M.: The linearization principle for the stability of solutions of quasilinear parabolic equations. Arch. Rat. Mech. An.77, 301–320 (1981)
Sinestrari, E.: On the abstract Cauchy problem of parabolic type in spaces of continuous functions. J. Math. An. Appl. (to appear)
Sobolevskiî, P.E.: Equations of parabolic type in a Banach space. Am. Math. Soc. Transl.49, 1–62 (1966)
Stewart, H.B.: Generation of analytic semigroups by strongly elliptic operators. Trans. Am. Math. Soc.199, 141–162 (1974)
Wahl, W. von: Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen Hölderstetiger Funktionen. Nachtr. Akad. Wiss. Göttingen Math. Phys. Kl.11, 231–258 (1972)
Wahl, W. von: Einige Bemerkungen zu meiner Arbeit „Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen Hölderstetiger Funktionen”. Manuscripta Math.11, 199–201 (1974)
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Lunardi, A. Abstract quasilinear parabolic equations. Math. Ann. 267, 395–415 (1984). https://doi.org/10.1007/BF01456097
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DOI: https://doi.org/10.1007/BF01456097