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Stabilization of solutions of abstract parabolic equations. (English) Zbl 0499.35059


MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
47H05 Monotone operators and generalizations
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References:

[1] J. L. Lions: Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod Gauthier-Villars, Paris, 1969. · Zbl 0189.40603
[2] F. E. Browder: Non-linear initial value problems. Ann. of Math., 82, (1965), 51 - 87. · Zbl 0131.13502 · doi:10.2307/1970562
[3] F. E. Browder: Existence theorems for nonlinear partial differential equations, Global analysis. Proc. Symp. Pure Math. Vol. 16, Amer. Math. Soc. (1970), 1 - 60.
[4] H. Brézis: Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Nonlinear Functional Analysis. E. Zarantonello Acad. Press (1971).
[5] V. Barbu: Semi-groups of nonlinear contractions in Banach spaces. (Rumanian), Academia, Bucharest, 1974. · Zbl 0276.47044
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[8] J. Kačur: Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order I, II. Czechoslovak Math. J., to appear.
[9] J. Nečas: Application of Rothe’s method to abstract parabolic equations. Czechoslovak Math. J., · Zbl 0311.35059
[10] J. Kačur: Applications of Rothe’s method to nonlinear evolution equations. Mat. Časopis Sloven. Akad. Vied, 25, (1975), N-1, 63-81.
[11] C. V. Pao: On the stability of nonlinear operator differential equations and applications. Arch. Rational Mech. Anal. 35, (1969), 30-46. · Zbl 0187.08801
[12] J. A. Dubinskij: Quasilinear elliptic and parabolic equations of arbitrary order. (Russian), Uspehi Mat. Nauk, 23, 1 (1968), 45-90. · Zbl 0162.42303 · doi:10.1070/RM1968v023n01ABEH001233
[13] R. Bellman: Stability theory of differential equations. New York-Toronto-London, 1953. · Zbl 0053.24705
[14] M. A. Krasnoselskij: Topological methods in the theory of nonlinear integral equations. Pergamon Press, New York, 1964.
[15] K. Yosida: Functional Analysis. Springer, Berlin-Heidelberg-New York, 1969. · Zbl 0152.32102
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