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Bibliography
Bellman, R., On the existence and boundedness of solutions of nonlinear partial differential equations of parabolic type. Trans. Am. Math. Soc. 64, 21–44 (1948).
Friedman, A., Convergence of solutions of parabolic equations to a steady state. J. Math. Mech. 8, 57–76 (1959).
Friedman, A., Partial Differential Equations. New York: Holt, Rinehart and Winston 1969.
Fujita, H., On the nonlinear equations Δu + e u = 0 and ∂v/∂t = Δv + e v. Bull. Am. Math. Soc. 75, 132–135 (1969).
Fujita, H., On the Asymptotic Stability of Solutions of the Equation v t = Δv + e v. Proc. Int. Conf. Funct. Anal. Rel. Topics, Tokyo 1969, 252–259, University of Tokyo Press (1970).
Gel'fand, I.M, Some problems in the theory of quasilinear equations. Am. Math. Soc. Transl. (2) 29, 295–381 (1963).
Iooss, G., Théorie non linéaire de la stabilité des écoulements laminaires dans le cas de ≪l'échange des stabilités≫. Arch. Rational Mech. Anal. 40, 166–208 (1971).
Kato, T., Perturbation Theory for Linear Operators. New York: Springer-Verlag, Berlin, Heidelberg 1966.
Kato, T., & H. Fujita, On the non-stationary Navier-Stokes system. Rend. Sem. Mat. Univ. Padova 32, 243–260 (1962)
Kielhöfer, H., Hilbertraum-Theorie für fastlineare Anfangswertprobleme. Dissertation, Bochum (1972).
Kielhöfer, H., Halbgruppen und semilineare Anfangs-Randwertprobleme. Manuscripta Math. 12, 121–152 (1974).
Kirchgässner, K., & H. Kielhöfer, Stability and bifurcation in fluid dynamics. Rocky Mountain J. Math. (2) 3, 275–318 (1973).
Lions, J.L., Sur les espaces d'interpolation; Dualité. Math. Scand. 9, 147–177 (1961).
Lions, J.L., & E. Magenes, Problèmes aux Limites Non Homogènes et Applications, 1. Paris: Dunod 1968.
Narasimhan, R., On the asymptotic stability of solutions of parabolic differential equations. J. Rational Mech. Anal. 3, 303–313 (1954).
Peetre, J., Espaces d'interpolation et théorème de Soboleff. Ann. Inst. Fourier (1) 16, 279–317 (1966).
Prodi, G., Teoremi di tipo locale per il sistema di Navier-Sokes e stabilità delle soluzioni stazionarie. Rend. Sem. Mat. Univ. Padova 32, 374–397 (1962).
Roseau, M., Vibrations Non Linéaires et Théorie de la Stabilité. New York: Springer Verlag, Berlin, Heidelberg 1966.
Sattinger, D.H., The mathematical problem of hydrodynamic stability. J. Math. Mech. 19, 797–817 (1970).
Sobolevskii, P.E., Equations of parabolic type in Banach space. Am. Math. Soc. Transl. (2), 1–62 (1966).
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Communicated by J. Serrin
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Kielhöfer, H. Stability and semilinear evolution equations in Hilbert space. Arch. Rational Mech. Anal. 57, 150–165 (1974). https://doi.org/10.1007/BF00248417
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DOI: https://doi.org/10.1007/BF00248417