Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms

Jian Dang; Qingying Hu; Hongwei Zhang

doi:doi:10.11648/j.ijamtp.20160204.13

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Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms

Jian Dang, Qingying Hu, Hongwei Zhang

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)

Received: 21 August 2016 Accepted: 29 August 2016 Published: 14 October 2016

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Abstract

In this paper, we are concerned with one-dimensional Timoshenko model for a beam with nonlinear damping and source terms. We establish a blow-up result when the initial energy is positive and the initial data is not in a potential well. Under arbitrary positive initial energy, we also prove a finite-time blow-up result for a special case.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4)
DOI	10.11648/j.ijamtp.20160204.13
Page(s)	41-45
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Timoshenko System, Source Term, Damping Term, Blow-up

References

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[4]	N. E. Tatar. Stabilization of a viscoelastic Timoshenko beam. Applicable Analysis, 92 (1) (2013), 27-43.
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[10]	C. Gorgi and F. M.Vegni. Uniform energy estimates for a semilinear evolution equation of the Mindlin-Timoshenko beam with memory. Mathematical and Computer Modelling, 39 (2004), 1005-1021.
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[13]	P. Pei, M. A. Rammaha, D. Toundykov. Global well-posedness and stability of semilinear Mindlin-Timoshenko systems. J. Math. Anal. Appl. 418 (2014), 535-568.
[14]	D. H. Sattinger. On global solutions of nonlinear hyperbolic equation. Arch. Rational Mech. Anal. 30 (1968), 108-172.
[15]	I. E. Payne, D. H. Sattinger. Saddle points and instability of nonlinear hyperbolic equations. Israel J. Math. 22 (1975), 273-303.
[16]	K. Agre, M. A. Rammaha. System of nonlinear wave equation with damping and source terms. Differential and Integral Equation, 19 (1) (2006), 1235-1270.
[17]	B. Said-Houari. Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms. Differential and Integral Equation, 23 (1-2) (2010), 29-92.
[18]	E. Vitillaro. Global nonexistence theorems for a class of evolution equation with dissipations. Arch. Rational Mech Anal. 149 (1999), 155-182.
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APA Style

Jian Dang, Qingying Hu, Hongwei Zhang. (2016). Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 41-45. https://doi.org/10.11648/j.ijamtp.20160204.13

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ACS Style

Jian Dang; Qingying Hu; Hongwei Zhang. Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 41-45. doi: 10.11648/j.ijamtp.20160204.13

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AMA Style

Jian Dang, Qingying Hu, Hongwei Zhang. Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. Int J Appl Math Theor Phys. 2016;2(4):41-45. doi: 10.11648/j.ijamtp.20160204.13

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@article{10.11648/j.ijamtp.20160204.13,
  author = {Jian Dang and Qingying Hu and Hongwei Zhang},
  title = {Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {41-45},
  doi = {10.11648/j.ijamtp.20160204.13},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.13},
  abstract = {In this paper, we are concerned with one-dimensional Timoshenko model for a beam with nonlinear damping and source terms. We establish a blow-up result when the initial energy is positive and the initial data is not in a potential well. Under arbitrary positive initial energy, we also prove a finite-time blow-up result for a special case.},
 year = {2016}
}

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TY  - JOUR
T1  - Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms
AU  - Jian Dang
AU  - Qingying Hu
AU  - Hongwei Zhang
Y1  - 2016/10/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.13
DO  - 10.11648/j.ijamtp.20160204.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 41
EP  - 45
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.13
AB  - In this paper, we are concerned with one-dimensional Timoshenko model for a beam with nonlinear damping and source terms. We establish a blow-up result when the initial energy is positive and the initial data is not in a potential well. Under arbitrary positive initial energy, we also prove a finite-time blow-up result for a special case.
VL  - 2
IS  - 4
ER  -

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Author Information

Jian Dang

Department of Mathematics, Henan University of Technology, Zhengzhou, China
Qingying Hu

Department of Mathematics, Henan University of Technology, Zhengzhou, China
Hongwei Zhang

Department of Mathematics, Henan University of Technology, Zhengzhou, China

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APA Style

Jian Dang, Qingying Hu, Hongwei Zhang. (2016). Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 41-45. https://doi.org/10.11648/j.ijamtp.20160204.13

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ACS Style

Jian Dang; Qingying Hu; Hongwei Zhang. Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 41-45. doi: 10.11648/j.ijamtp.20160204.13

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AMA Style

Jian Dang, Qingying Hu, Hongwei Zhang. Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms. Int J Appl Math Theor Phys. 2016;2(4):41-45. doi: 10.11648/j.ijamtp.20160204.13

Copy | Download

@article{10.11648/j.ijamtp.20160204.13,
  author = {Jian Dang and Qingying Hu and Hongwei Zhang},
  title = {Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {4},
  pages = {41-45},
  doi = {10.11648/j.ijamtp.20160204.13},
  url = {https://doi.org/10.11648/j.ijamtp.20160204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160204.13},
  abstract = {In this paper, we are concerned with one-dimensional Timoshenko model for a beam with nonlinear damping and source terms. We establish a blow-up result when the initial energy is positive and the initial data is not in a potential well. Under arbitrary positive initial energy, we also prove a finite-time blow-up result for a special case.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Blow-up of Solutions for Semilinear Timoshenko System with Damping and Source Terms
AU  - Jian Dang
AU  - Qingying Hu
AU  - Hongwei Zhang
Y1  - 2016/10/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160204.13
DO  - 10.11648/j.ijamtp.20160204.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 41
EP  - 45
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160204.13
AB  - In this paper, we are concerned with one-dimensional Timoshenko model for a beam with nonlinear damping and source terms. We establish a blow-up result when the initial energy is positive and the initial data is not in a potential well. Under arbitrary positive initial energy, we also prove a finite-time blow-up result for a special case.
VL  - 2
IS  - 4
ER  -

Copy | Download