Publication Cover
Applicable Analysis
An International Journal
Volume 77, 2001 - Issue 3-4
21
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On Existence of global solutions for the carrier model with nonlinear damping and source terms

Nonlinear damping and source terms

, &
Pages 305-318 | Received 01 Jun 2000, Published online: 02 May 2007

References

  • Bellman , R. 1971 . Inequalities , Springer—Verlag .
  • Carrier , G. F. 1945 . On the nonlinear vibrations problem, of the elastic siring . Quart. Appl. Math , 3 : 157 – 165 .
  • Cousin , A. T. , Frota , C. L. , Lar'kin , N. A. and Medeiros , L. A. 1997 . On the abstract model of the Kirchhoff—Carrier equation . Comm, Appl. Anal , 1 : 389 – 404 .
  • Frota , C. L. , Cousin , A. T. and Lar'kin , N. A. 1999 . Existence of global solutions and energy decay for the Carrier equation with dissipative term . Diff. Int. Eqs , 12 ( 4 ) : 453 – 469 .
  • Kirchhoff , G. 1883 . Vorlesungen über Mechanik , Tauber Leipzig .
  • Lar'kin , N.A. 1981 . Solvability in the large of boundary value problems for a class of quasilinear hyperbolic equations . Siberian Math, J , 22 : 82 – 88 .
  • Lions , J. L. 1969 . Quelques méthode de Résolution des problème aux limites Nonlinéaire , Paris : Dunod Gauthier—Villars .
  • Matsuyama , T. and Ikehata , R. 1996 . On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms . J. Math. Anal. Appl , 204 : 729 – 753 .
  • Menzala , G. P. 1979 . On classical solutions of quasilinear hyperbolic equations . Nonlinear Anal , 3 : 613 – 627 .
  • Newman , W. G. 1995 . Global solution of a nonlinear string equation . J. Math. Anal. Appl , 192 : 689 – 704 .
  • Narasimha , K. 1968 . Nonlinear vibration of an elastic string . J. Sound Vib , 8 : 134 – 146 .
  • Nishihara , K. and Yamada , Y. 1990 . On global solutions of some degenerate quasilinear hyperbolic equation with dissipative damping 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 .
  • Park , J.Y. and Bae , J.J. 1998 . On the existence of solutions of the degenerate wave equations with nonlinear damping terms . J. Korean Math. Soc , 35 ( 2 ) : 465 – 489 .
  • Park , J. Y. and Jung , I. H. 1999 . On a class of quasilinear hyperbolic equations and Yosida approximations . Indian J. Pure Appl, Math , 30 ( 11 ) : 1093 – 1106 .
  • Yamada , Y. 1996 . Some nonlinear degenerate wave equation . Nonlinear Anal , 11 ( 11 ) : 1155 – 1168 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.