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Decay of solutions of some nonlinear evolution equations. (English) Zbl 0376.34051

MSC:
34G99ODE in abstract spaces
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References:
[1] Biroli, M.: Solutiones presque periodiques des inequations devolution paraboliques. Ann. mat. 88, 51-70 (1971) · Zbl 0221.35037
[2] Caughy, T. K.; Ellison, J.: Existence, uniqueness and stability of solutions of a class of nonlinear partial differential equations. J. math. Anal. appl. 51, 1-32 (1975) · Zbl 0306.35029
[3] Dubinskii, J. A.: Quasilinear elliptic and parabolic equations of arbitrary order. Russian math. Surveys 23, 45-91 (1968)
[4] Greenberg, J. M.; Maccamy, R. C.; Mizel, V. J.: On the existence, uniqueness and stability of solutions of the equation ${\lambda}'(ux)uxx + {\lambda}$uxtx = \varrho0utt. J. math. Mech. 17, 707-728 (1968)
[5] Lions, J. L.: Quelques méthodes des résolution des problèmes aux limites non linéaires. (1969)
[6] M. Nakao, On the existence of bounded solution for nonlinear evolution equation of parabolic type, to appear. · Zbl 0362.35048
[7] M. Nakao, Asymptotic stability of bounded or almost periodic solutions of the wave equation with a nonlinear dissipative term, J. Math. Anal. Appl., in press. · Zbl 0347.35013
[8] M. Nakao, Convergence of solutions of the wave equation with a nonlinear dissipative term to the steady state, to appear. · Zbl 0359.35052
[9] Nakao, M.; Nanbu, T.: Existence of global (bounded) solutions for some nonlinear evolution equations of second order. Math. rep. College gen. Educ. kyushu univ. 10, No. No. 1, 67-75 (1975)
[10] Prouse, G.: Periodic or almost periodic solutions of a nonlinear functional equation, IV. Rend. accad. Naz. lincei 54, 3-10 (1968)
[11] Strauss, W. A.: On continuity of functions with values in various Banach spaces. Pacific J. Math. 19, No. No. 3, 543-551 (1966) · Zbl 0185.20103
[12] Strauss, W. A.: Evolution equations non-linear in the time derivative. J. math. Mech. 15, No. No. 1. 1, 49-82 (1966) · Zbl 0138.40001
[13] Strauss, W. A.: The energy method in nonlinear partial differential equations. Notas mat. (1969) · Zbl 0233.35001
[14] Tsutsumi, M.: Some nonlinear evolution equations of second order. Proc. Japan acad. 47, 950-955 (1971) · Zbl 0258.35017
[15] Tsutsumi, M.: Existence and non existence of a global solution for nonlinear parabolic equations. Publ. res. Inst. math. Sci., Kyoto univ. 8, 211-229 (1972) · Zbl 0248.35074