Global in time solutions to quasilinear telegraph equations involving operators with time delay

Eduard Feireisl

Applications of Mathematics (1991)

  • Volume: 36, Issue: 6, page 456-468
  • ISSN: 0862-7940

Abstract

top
The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.

How to cite

top

Feireisl, Eduard. "Global in time solutions to quasilinear telegraph equations involving operators with time delay." Applications of Mathematics 36.6 (1991): 456-468. <http://eudml.org/doc/15693>.

@article{Feireisl1991,
abstract = {The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.},
author = {Feireisl, Eduard},
journal = {Applications of Mathematics},
keywords = {quasilinear telegraph equations; bounded solutions; time-periodic solutions; time delay; small global solution; abstract evolution equation; nonlinear coefficients; nonlinear right-hand side; small global solution; quasilinear telegraph equations; bounded solutions; time-periodic solutions; abstract evolution equation; nonlinear coefficients; nonlinear right-hand side; time-delay},
language = {eng},
number = {6},
pages = {456-468},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global in time solutions to quasilinear telegraph equations involving operators with time delay},
url = {http://eudml.org/doc/15693},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Global in time solutions to quasilinear telegraph equations involving operators with time delay
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 6
SP - 456
EP - 468
AB - The existence of small global (in time) solutions to an abstract evolution equation containing a damping term is proved. The result is then applied to fully nonlinear telegraph equations and to nonlinear equations involving operators with time delay.
LA - eng
KW - quasilinear telegraph equations; bounded solutions; time-periodic solutions; time delay; small global solution; abstract evolution equation; nonlinear coefficients; nonlinear right-hand side; small global solution; quasilinear telegraph equations; bounded solutions; time-periodic solutions; abstract evolution equation; nonlinear coefficients; nonlinear right-hand side; time-delay
UR - http://eudml.org/doc/15693
ER -

References

top
  1. A. B. Aliev, The global solvability of unilateral problems for quasilinear operators of the hyperbolic type (Russian), Dokl. Akad. Nauk SSSR 298 (5) (1988), 1033-1036. (1988) MR0939671
  2. A. Arosio, Global (in time) solution of the approximate non-linear string equation of G. F. Carrier and R. Narasimha, Comment. Math. Univ. Carolinae 26 (1) (1985), 169-172. (1985) MR0797299
  3. A. Arosio, 10.1007/BF00275732, Arch. Rational Mech. Anal. 86 (2) (1984), 147-180. (1984) Zbl0563.35041MR0751306DOI10.1007/BF00275732
  4. P. Biler, 10.1016/0362-546X(86)90071-4, Nonlinear Anal. 10 (9) (1984), 839-842. (1984) MR0856867DOI10.1016/0362-546X(86)90071-4
  5. E. Feireisl, Small time-periodic solutions to a nonlinear equation of a vibrating string, Apl. mat. 32 (6) (1987), 480-490. (1987) Zbl0653.35063MR0916063
  6. Z. Kamont J. Turo, 10.1007/BF01769218, Ann. Mat. Рurа Appl. 143 (4) (1986), 235 - 246. (1986) MR0859605DOI10.1007/BF01769218
  7. T. Kato, 10.1007/BFb0067080, Lectures Notes in Mathematics 448, 25 - 70. Springer, Berlin 1975. (1975) MR0407477DOI10.1007/BFb0067080
  8. P. Krejčí, Hard implicit function theorem and small periodic solutions to partial differential equations, Comment. Math. Univ. Carolinae 25 (1984), 519-536. (1984) MR0775567
  9. J. L. Lions E. Magenes, Problèmes aux limites non homogènes et applications I, Dunod, Paris 1968. (1968) 
  10. A. Matsumura, 10.2977/prims/1195189813, Publ. RIMS Kyoto Univ. 13 (1977), 349-379. (1977) Zbl0371.35030MR0470507DOI10.2977/prims/1195189813
  11. L. A. Medeiros, 10.1016/0022-247X(79)90192-6, J. Math. Anal. Appl. 69 (1) (1979), 252-262. (1979) Zbl0407.35051MR0535295DOI10.1016/0022-247X(79)90192-6
  12. H. Petzeltová M. Štědrý, Time periodic solutions of telegraph equations in n spatial variables, Časopis Pěst. Mat. 109 (1984), 60-73. (1984) MR0741209
  13. H. Poorkarimi J. Wiener, Bounded solutions of nonlinear hyperbolic equations with delay, Lecture Notes in Pure and Appl. Math. 109 (Dekker), 1987. (1987) MR0912327
  14. P. H. Rabmowitz, 10.1002/cpa.3160220103, Comm. Pure Appl. Math. 22 (1969), 15-39. (1969) DOI10.1002/cpa.3160220103
  15. Y. Shibata Y. Tsutsumi, 10.1016/0362-546X(87)90051-4, Nonlinear Anal. 11 (3) (1987), 335-365. (1987) MR0881723DOI10.1016/0362-546X(87)90051-4
  16. M. Štědrý, Small time-periodic solutions to fully nonlinear telegraph equations in more spatial dimensions, preprint. Ann. Inst. Henri Poincaré 6 (3) (1989), 209-232. (1989) MR0995505
  17. Vejvoda O., al., Partial differential equations: Time periodic solutions, Martinus Nijhoff Publ., 1982. (1982) Zbl0501.35001

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.