Exponential stability for Timoshenko model with thermal effect

Luiz Gutemberg Rosário Miranda; Bruno Magalhães Alves

Applications of Mathematics (2025)

  • Issue: 2, page 149-168
  • ISSN: 0862-7940

Abstract

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We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.

How to cite

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Miranda, Luiz Gutemberg Rosário, and Alves, Bruno Magalhães. "Exponential stability for Timoshenko model with thermal effect." Applications of Mathematics (2025): 149-168. <http://eudml.org/doc/299985>.

@article{Miranda2025,
abstract = {We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.},
author = {Miranda, Luiz Gutemberg Rosário, Alves, Bruno Magalhães},
journal = {Applications of Mathematics},
keywords = {Timoshenko beams; thermoelastic; well-posedness; semigroup; exponential decay; Lyapunov functional},
language = {eng},
number = {2},
pages = {149-168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Exponential stability for Timoshenko model with thermal effect},
url = {http://eudml.org/doc/299985},
year = {2025},
}

TY - JOUR
AU - Miranda, Luiz Gutemberg Rosário
AU - Alves, Bruno Magalhães
TI - Exponential stability for Timoshenko model with thermal effect
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 149
EP - 168
AB - We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.
LA - eng
KW - Timoshenko beams; thermoelastic; well-posedness; semigroup; exponential decay; Lyapunov functional
UR - http://eudml.org/doc/299985
ER -

References

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  1. Júnior, D. S. Almeida, Elishakoff, I., Ramos, A. J. A., Miranda, L. G. R., 10.1093/imamat/hxz014, IMA J. Appl. Math. 84 (2019), 763-796. (2019) Zbl1476.74067MR3987834DOI10.1093/imamat/hxz014
  2. Júnior, D. S. Almeida, Santos, M. L., Rivera, J. E. Muñoz, 10.1002/mma.2741, Math. Methods Appl. Sci. 36 (2013), 1965-1976. (2013) Zbl1273.74072MR3091687DOI10.1002/mma.2741
  3. Júnior, D. S. Almeida, Santos, M. L., Rivera, J. E. Muñoz, 10.1007/s00033-013-0387-0, Z. Angew. Math. Phys. 65 (2014), 1233-1249. (2014) Zbl1316.35044MR3279528DOI10.1007/s00033-013-0387-0
  4. Apalara, T. A., Messaoudi, S. A., Mustafa, M. I., Energy decay in thermoelasticity type III with viscoelastic damping and delay term, Electron. J. Differ. Equ. 2012 (2012), Article ID 128, 15 pages. (2012) Zbl1254.35144MR2967193
  5. Borichev, A., Tomilov, Y., 10.1007/s00208-009-0439-0, Math. Ann. 347 (2010), 455-478. (2010) Zbl1185.47044MR2606945DOI10.1007/s00208-009-0439-0
  6. Casas, P. S., Quintanilla, R., 10.1016/j.mechrescom.2005.02.015, Mech. Res. Commun. 32 (2005), 652-658. (2005) Zbl1192.74156MR2158183DOI10.1016/j.mechrescom.2005.02.015
  7. Gearhart, L., 10.1090/S0002-9947-1978-0461206-1, Trans. Am. Math. Soc. 236 (1978), 385-394. (1978) Zbl0326.47038MR0461206DOI10.1090/S0002-9947-1978-0461206-1
  8. Huang, F., Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differ. Equations 1 (1985), 43-56. (1985) Zbl0593.34048MR0834231
  9. Rivera, J. E. Muñoz, Racke, R., 10.1016/S0022-247X(02)00436-5, J. Math. Anal. Appl. 276 (2002), 248-278. (2002) Zbl1106.35333MR1944350DOI10.1016/S0022-247X(02)00436-5
  10. Prüss, J., 10.1090/S0002-9947-1984-0743749-9, Trans. Am. Math. Soc. 284 (1984), 847-857. (1984) Zbl0572.47030MR0743749DOI10.1090/S0002-9947-1984-0743749-9
  11. Soufyane, A., 10.1016/S0764-4442(99)80244-4, C. R. Acad. Sci., Paris, Sér. I, Math. 328 (1999), 731-734 French. (1999) Zbl0943.74042MR1680836DOI10.1016/S0764-4442(99)80244-4
  12. Timoshenko, S. P., 10.1080/14786442108636264, Phil. Mag. (6) 41 (1921), 744-746. (1921) DOI10.1080/14786442108636264

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