Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings
Rendiconti del Seminario Matematico della Università di Padova, Volume 106 (2001), p. 185-205
@article{RSMUP_2001__106__185_0,
     author = {Ghisi, Marina},
     title = {Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {106},
     year = {2001},
     pages = {185-205},
     zbl = {1072.35129},
     mrnumber = {1876220},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2001__106__185_0}
}
Ghisi, Marina. Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings. Rendiconti del Seminario Matematico della Università di Padova, Volume 106 (2001) pp. 185-205. http://www.numdam.org/item/RSMUP_2001__106__185_0/

[1] A. Arosio, Averaged evolution equations. The Kirchhoff string and its treatment in scales of Banach spaces, proceedings of the «2nd workshop on functional-analytic methods in complex analysis» (Trieste, 1993), World Scientific, Singapore. | MR 1414220

[2] E.H. De Brito, The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability, Applicable Analysis, 13 (1982), pp. 219-233. | MR 663775 | Zbl 0458.35065

[3] E.H. De Brito, Decay estimates for the generalized damped extensible string and beam equation, Nonlinear Analysis, 8 (1984), pp. 1489-1496. | MR 769410 | Zbl 0524.35026

[4] P. D'Ancona - S. Spagnolo, Nonlinear perturbations of the Kirchhoff equation, Comm. Pure Appl. Math., 47 (1994), pp. 1005-1029. | MR 1283880 | Zbl 0807.35093

[5] M. Ghisi, Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations, Preprint Dip. Mat. Univ. Pisa N° 2.293.1099 (1998). | MR 1961549 | Zbl 1028.35113

[6] M. Ghisi - M. Gobbino, Global Existence for a Mildly Degenerate Dissipative Hyperbolic Equation of Kirchhoff Type, Preprint Dip. Mat. Univ. Pisa (1997).

[7] M. Hosoya - 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), pp. 239-250. | MR 1127082 | Zbl 0783.35038

[8] R. Ikehata, A note on the global solvability of solutions to some nonlinear wave equations with dissipative terms, Differential Integral Equations, 8 (1995), pp. 607-616. | MR 1306578 | Zbl 0812.35081

[9] M. Nakao, A Difference Inequality and its Application to Nonlinear Evolution Equations, J. Math. Soc. Japan, 30 (1978), pp. 747-762. | MR 513082 | Zbl 0388.35007

[10] K. Nishihara, Global Existence and Asymptotic Behaviour of the Solution of Some Quasilinear Hyperbolic Equation with Linear Damping, Funkcial. Ekvac., 32 (1989), pp. 343-355. | MR 1040163 | Zbl 0702.35165

[11] K. Nishihara - Y. YAMADA, On Global Solutions of some Degenerate Quasilinear Hyperbolic Equations with Dissipative Terms, Funkcial. Ekvac., 33 (1990), pp. 151-159. | MR 1065473 | Zbl 0715.35053

[12] K. Ono, Global Existence and Decay Properties of Solutions of Some Mildly Degenerate Nonlinear Dissipative Kirchhoff Strings, Funkcial. Ekvac., 40 (1997), pp. 255-270. | MR 1480278 | Zbl 0891.35100

[13] K. Ono, Global Existence, Decay and Blowup Of Solutions for Some Mildly Degenerate Nonlinear Kirchhoff Strings, J. Diff. Eq., 137 (1997), pp. 273-301. | MR 1456598 | Zbl 0879.35110

[14] Y. Yamada, On some quasilinear wave equations with dissipative terms, Nagoya Math. J., 87 (1982), pp. 17-39. | MR 676584 | Zbl 0501.35058

[15] S. Spagnolo, The Cauchy problem for the Kirchhoff equation, Rend. Sem. Fis. Matem. di Milano, 62 (1992), pp. 17-51. | MR 1293773 | Zbl 0809.35061

[16] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics«, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1988. | MR 953967 | Zbl 0662.35001