Journal of Mathematical Sciences: Advances and Applications[1] A. Arosio and S. Garavaldi, On the mildly degenerate Kirchhoff
string, Math. Methods Appl. Sci. 14 (1991), 177-195.
[2] A. Arosio and S. Panizzi, On the well-posedness of the Kirchhoff
string, Trans. Amer. Math. Soc. 348 (1996), 305-330.
[3] H. R. Crippa, On local solutions of some mildly degenerate
hyperbolic equations, Nonlinear Analysis 21 (1993), 565-574.
[4] R. W. Dickey, Infinite systems of nonlinear oscillation equations
with linear damping, SIAM J. Appl. Math. 19 (1970), 208-214.
[5] M. Ghisi and M. Gobbino, Hyperbolic-parabolic singular
perturbation for mildly degenerate Kirchhoff equations: Time-decay
estimates, J. Differential Equations 245 (2008), 2979-3007.
[6] M. Hosoya and Y. Yamada, On some nonlinear wave equations, II,
Global existence and energy decay of solutions, J. Fac. Sci. Univ.
Tokyo Sect. IA Math. 38 (1991), 239-250.
[7] H. Ishii, Asymptotic stability and blowing-up of solutions of some
nonlinear equations, J. Differential Equations 26 (1977), 291-319.
[8] G. Kirchhoff, Vorlesungen über Mechanik, Teubner, Leipzig,
1883.
[9] M. Nakao, A difference inequality and its application to nonlinear
evolution equations, J. Math. Soc. Japan 30 (1978), 747-762.
[10] M. Nakao and K. Ono, Existence of global solutions to the Cauchy
problem for the semilinear dissipative wave equations, Math. Z. 214
(1993), 325-342.
[11] R. Narasimha, Nonlinear vibration of an elastic string, J. Sound
Vib. 8 (1968), 134-146.
[12] K. Nishihara, Decay properties of solutions of some quasilinear
hyperbolic equations with strong damping, Nonlinear Anal. 21 (1993),
17-21.
[13] K. Nishihara and Y. Yamada, On global solutions of some
degenerate quasilinear hyperbolic equations with dissipative terms,
Funkcial. Ekvac. 33 (1990), 151-159.
[14] K. Ono, Global existence and decay properties of solutions for
some mildly degenerate nonlinear dissipative Kirchhoff strings,
Funkcial. Ekvac. 40 (1997), 255-270.
[15] K. Ono, On global existence, asymptotic stability and blowing-up
of solutions for some degenerate nonlinear wave equations of Kirchhoff
type with a strong dissipation, Math. Methods Appl. Sci. 20 (1997),
151-177.
[16] K. Ono, Asymptotic behaviour for degenerate nonlinear Kirchhoff
type equations with damping, Funkcial. Ekvac. 43 (2000), 381-393.
[17] K. Ono, On sharp decay estimates of solutions for mildly
degenerate dissipative wave equations of Kirchhoff type, Math. Methods
Appl. Sci. 34 (2011), 1339-1352.
[18] L. E. Payne and D. H. Sattinger, Saddle points and instability of
nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303.
[19] M. Tsutsumi, On solutions of semilinear differential equations in
a Hilbert space, Math. Japon. 17 (1972), 173-193.
[20] Y. Yamada, On the decay of solutions for some nonlinear evolution
equations of second order, Nagoya Math. J. 73 (1979), 69-98.
