Authors:
Ducival Carvalho PereiraDepartment of Mathematics, State University of Pará, 66113-010, Belém, Brazil

Search for other papers by Ducival Carvalho Pereira in
Current site
Google Scholar
PubMed
Close
,
Carlos Alberto RaposoDepartment of Mathematics, Federal University of Bahia, 40170-115, Salvador, Brazil

Search for other papers by Carlos Alberto Raposo in
Current site
Google Scholar
PubMed
Close
, and
Huy Hoang NguyenCollege of Natural Sciences, University of Texas at Austin, 78712, Texas, USA

Search for other papers by Huy Hoang Nguyen in
Current site
Google Scholar
PubMed
Close
Open access

This manuscript deals with the global existence and asymptotic behavior of solutions for a Kirchhoff beam equation with internal damping. The existence of solutions is obtained by using the Faedo-Galerkin method. Exponential stability is proved by applying Nakao’s theorem.

  • [1]

    AUBIN, J. P. Un thèoréme de compacité. C. R. Acad. Sci. 256 (1963), 50425044.

  • [2]

    BERGER, M. A new approach to the large deflection of plate. J. Appl. Mech. 22 (1955), 465472.

  • [3]

    BURGREEN, D. Free vibrations of a pin-ended column with constant distance between pin ends. J. Appl. Mech. 18 (1951), 135139.

  • [4]

    CAVALCANTI, M. M., CAVALCANTI, V. D., and SORIANO, J. A. Global existence and asymptotic stability for the nonlinear and generalized damped extensible plate equation. Commun. Contemp. Math. 6 (2004), 705731.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [5]

    CODDINGTON, E., and LEVINSON, N. Theory of Ordinary Differential Equations. McGraw-Hill Inc., New York, 1955.

  • [6]

    EISLEY, J. Nonlinear vibration of beams and rectangular plates. Z. Angew. Math. Phys. 15 (1964), 167175.

  • [7]

    KIRCHHOFF, G. Vorlesungen uber mechanik. Tauber, Leipzig, 1883.

  • [8]

    LIONS, J. L. Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier Villars, Paris, 1969.

  • [9]

    MEDEIROS, L. A., LIMACO, J., and MENEZES, S. B. Vibrations of elastic strings: mathematical aspects, part one. J. Comput. Anal. Appl. 4 (2002), 91127.

    • Search Google Scholar
    • Export Citation
  • [10]

    MIKLIN, S. Variational Methods in Mathematical Physics. Pergamon Press, Oxford, 1964.

  • [11]

    MIRANDA, M. M., and JUTUCA, P. S. G. Existence and boundary stabilization of solutions for the kirchhoff equation. Commun. Partial Differential Equations 24 (1999), 17591880.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [12]

    MIRANDA, M. M., LOUREIRO, A. T., and MEDEIROS, L. A. Nonlinear pertubartions of the kirchoff equations. Electron. J. Differ. Equ. 77 (2017), 121.

    • Search Google Scholar
    • Export Citation
  • [13]

    NAKAO, M. A difference inequalit and its application to nonlinear evolution equation. J. Math. Soc. Japan 30 (1978), 747762.

  • [14]

    NAKAO, M. Decay estimates for some semilinear wave equations with degenerate dissipative terms. Funkc. Ekvacioj 30 (1987), 135145.

  • [15]

    PEREIRA, D. C., NGUYEN, H. H., RAPOSO, C. A., and MARANHAO, C. H. M. On the solutions for an extensible beam equation with internal damping and source terms. Differ. Equ. Appl. 11 (2019), 367377.

    • Search Google Scholar
    • Export Citation
  • [16]

    SIMON, J. Compact sets in the space lp(o,t;b). Ann. Mat. Pura Appl. 146 (1986), 6596.

  • [17]

    TARTAR, L. Topics in Nonlinear Analysis. Uni. Paris Sud. Dep. Math., Orsay, 1978.

  • [18]

    WOINOWSKY-KRIEGER, S. The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17 (1950), 3536.

  • [19]

    ZHIJIAN, Y. On an extensible beam equation with nonlinear damping and source terms. Ann. Mat. Pura Appl. 254 (2013), 39033927.

  • Collapse
  • Expand
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)