Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings

Marina Ghisi

Rendiconti del Seminario Matematico della Università di Padova (2001)

  • Volume: 106, page 185-205
  • ISSN: 0041-8994

How to cite

top

Ghisi, Marina. "Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings." Rendiconti del Seminario Matematico della Università di Padova 106 (2001): 185-205. <http://eudml.org/doc/108562>.

@article{Ghisi2001,
author = {Ghisi, Marina},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {185-205},
publisher = {Seminario Matematico of the University of Padua},
title = {Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings},
url = {http://eudml.org/doc/108562},
volume = {106},
year = {2001},
}

TY - JOUR
AU - Ghisi, Marina
TI - Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2001
PB - Seminario Matematico of the University of Padua
VL - 106
SP - 185
EP - 205
LA - eng
UR - http://eudml.org/doc/108562
ER -

References

top
  1. [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. MR1414220
  2. [2] E.H. De Brito, The damped elastic stretched string equation generalized: existence, uniqueness, regularity and stability, Applicable Analysis, 13 (1982), pp. 219-233. Zbl0458.35065MR663775
  3. [3] E.H. De Brito, Decay estimates for the generalized damped extensible string and beam equation, Nonlinear Analysis, 8 (1984), pp. 1489-1496. Zbl0524.35026MR769410
  4. [4] P. D'Ancona - S. Spagnolo, Nonlinear perturbations of the Kirchhoff equation, Comm. Pure Appl. Math., 47 (1994), pp. 1005-1029. Zbl0807.35093MR1283880
  5. [5] M. Ghisi, Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations, Preprint Dip. Mat. Univ. Pisa N° 2.293.1099 (1998). Zbl1028.35113MR1961549
  6. [6] M. Ghisi - M. Gobbino, Global Existence for a Mildly Degenerate Dissipative Hyperbolic Equation of Kirchhoff Type, Preprint Dip. Mat. Univ. Pisa (1997). Zbl1070.34077
  7. [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. Zbl0783.35038MR1127082
  8. [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. Zbl0812.35081MR1306578
  9. [9] M. Nakao, A Difference Inequality and its Application to Nonlinear Evolution Equations, J. Math. Soc. Japan, 30 (1978), pp. 747-762. Zbl0388.35007MR513082
  10. [10] K. Nishihara, Global Existence and AsymptoticBehaviour of the Solution of Some Quasilinear Hyperbolic Equation with Linear Damping, Funkcial. Ekvac., 32 (1989), pp. 343-355. Zbl0702.35165MR1040163
  11. [11] K. Nishihara - Y. YAMADA, On Global Solutions of some Degenerate Quasilinear Hyperbolic Equations with Dissipative Terms, Funkcial. Ekvac., 33 (1990), pp. 151-159. Zbl0715.35053MR1065473
  12. [12] K. Ono, Global Existence and DecayProperties of Solutions of Some Mildly Degenerate Nonlinear Dissipative Kirchhoff Strings, Funkcial. Ekvac., 40 (1997), pp. 255-270. Zbl0891.35100MR1480278
  13. [13] K. Ono, Global Existence, Decay and Blowup ofSolutions for Some Mildly Degenerate Nonlinear Kirchhoff Strings, J. Diff. Eq., 137 (1997), pp. 273-301. Zbl0879.35110MR1456598
  14. [14] Y. Yamada, On some quasilinear wave equations with dissipative terms, Nagoya Math. J., 87 (1982), pp. 17-39. Zbl0501.35058MR676584
  15. [15] S. Spagnolo, The Cauchy problem for the Kirchhoff equation, Rend. Sem. Fis. Matem. di Milano, 62 (1992), pp. 17-51. Zbl0809.35061MR1293773
  16. [16] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics«, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1988. Zbl0662.35001MR953967

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.