References
- Arosio , A. and Garavaldi , S. 1991 . On the mildly degenerate kirchhoff string . Math. Methods Appl. Sci , 14 : 177 – 195 .
- Arosio , A. and Panizzi , S. 1996 . On the well-posedness of the kirchhoff string . Trans. Amer. Math. Soc , 348 : 305 – 330 .
- Carrier , C.F. 1945 . On the non-linear viberation problem of the elastic string . Quart. Appl. Math , 3 : 157 – 165 .
- Kawashima , S. , NakaO , M. and Ono , K. 1995 . On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term . J. Math. Soc , 47 : 617 – 653 .
- Kirchhoff , G. 1883 . Vorlesungen über Mechanik . Teubner, Leipzig ,
- Lasiecka , I. and Tataru , D. 1993 . Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping . Differential Integral Equations , 6 : 507 – 533 .
- Nakao , M. 1978 . Asymptotic stability for some nonlinear evoulation equations of second order with unbounded dissipative terms . J. Diff. Eqns , 30 : 54 – 63 .
- Nakao , M. 1977 . Decay of solutions of some nonlinear evolution equations . J. Math. Anal. Appl , 60 : 542 – 549 .
- Nishihara , K. 1993 . Decay properties of solutions of some quasilinear hyperbolic equations with strong damping . Nonlinear Anal , 21 : 17 – 21 .
- Nishihara , K. and Ono , K. 1994 . Asymptotic behaviors of solutions of some nonlinear oscillation equations with strong damping . Adv. Math. Sci. Appl , 4 : 285 – 295 .
- Nishihara , K. and Yamada , Y. 1990 . On global solutions of some degenerate quasilinear hyperbolic equations with dissipative terms . Funkcial. Ekvac , 33 : 151 – 159 .
- Ono , K. 1997 . Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings . J.Diff. Eqs , 137 : 273 – 301 .
- Ono K. The time decay to the Cauchy problem for semilinear dissipative wave equations Adv.Math. Sci. Appl., to appear
- Redheffer , R. 1982 . A comparsion theorem for difference inequalities . J. Diff. Eqns , 44 : 111 – 117 .
- Strauss , W.A. 1966 . On continuity of functions with values in various Banach spaces . Pacific J. Math , 19 : 543 – 551 .
- Temam , R. 1988 . Infinite Dimensional Dynamical systems in Mechanics and physics . Applied Mathematical Sciences , 68
- Yamada , Y. 1982 . On some quasilinear wave equations with dissipative terms . Nagoya Math. J , 87 : 17 – 39 .
- Yamazaki , T. 1988 . On local solutions of some quasilinear degenerate hyperbolic equations . Funkcial Ekvac , 31 : 439 – 457 .