Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


first{Blow up for a Nonlinear Viscoelastic Wave Equation with Strong Damping, Source and Delay Termes }

Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 139--148 | DOI:10.5890/DNC.2022.03.012

normalsize Department of Mathematics, Faculty of Exact Sciences, University of El Oued, Algeria, Laboratory of pure and

applied Mathematics, Amar Teledji Laghouat University, Algeria

Download Full Text PDF

 

Abstract

References

  1. [1] Berrimi, S. and Messaoudi, S. (2006), Existence and decay of solutions of a viscoelastic equation with a nonlinear source, Nonlinear Analysis, 64, 2314-2331.
  2. [2]  Cavalcanti, M.M., Cavalcanti, D., and Ferreira, J. (2001), Existence and uniform decay for nonlinear viscoelastic equation with strong damping, Math. Meth. Appl. Sci., 24, 1043-1053.
  3. [3]  Cavalcanti, M.M., Cavalcanti, D., Filho, P.J.S., and Soriano, J.A. (2001), Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping, Differential and Integral Equations, 14, 85-116.
  4. [4]  Kafini, M. and Messaoudi, S.A. (2008), A blow-up result in a cauchy viscoelastic problem, Applied Mathematics Letters, 21, 549-553. http://dx.doi.org/10.1016/j.aml.2007.07.004.
  5. [5]  Kafini, M. and Messaoudi, S.A. (2018), Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Applicable Analysis, DOI: 10.1080/00036811.2018.1504029.
  6. [6]  Song, H.T. and Xue, D.S. (2014), Blow up in a Nonlinear Viscoelastic Wave Equation with Strong Damping, Nonlinear Analysis, 109, 245-251. http://dx.doi.org/10.1016/j.na.2014.06.012.
  7. [7]  Song, H.T. and Zhong, C.K. (2010), Blow-up of solutions of a nonlinear viscoelastic wave equation, Nonlinear Analysis: Real World Applications, 11, 3877-3883.\\ http://dx.doi.org/10.1016/j.nonrwa.2010.02.015.
  8. [8] Zennir, K. (2013), Exponential growth of solutions with $L_{p}$-norm of a nonlinear viscoelastic hyperbolic equation, J. Nonlinear Sci. Appl., 6, 252-262.
  9. [9] Guo, L., Yuan, Z., and Lin, G. (2015), Blow Up and Global Existence for a Nonlinear Viscoelastic Wave Equation with Strong Damping and Nonlinear Damping and Source terms, Applied Mathematics, 6, 806-816.
  10. [10]  Ball, J. (1977), Remarks on blow-up and nonexistence theorems for nonlinear evolutions equation, Quarterly Journal of Mathematics, 28, 473-486.
  11. [11]  Boulaaras, S., Choucha, A., Ouchenane, D., and Cherif, B. (2020), Blow up of solutions of two singular nonlinear viscoelastic equations with general source and localized frictional damping terms, Advances in Difference Equations, 2020, 310. https://doi.org/10.1186/s13662-020-02772-0.
  12. [12]  Choucha, A., Ouchenane, D., and Boulaaras, S. (2020), Blow-up of a nonlinear viscoelastic wave equation with distributed delay combined with strong damping and source terms, J. Nonlinear Funct. Anal., Article ID 31 https://doi.org/10.23952/jnfa.2020.31.
  13. [13]  Messaoudi, S.A. (2006), Blow up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation, Journal of Mathematical Analysis and Applications, 320,902-915.
  14. [14]  Piskin, E. and Yuksekkaya, H. (2020), Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 1-14, DOI: 10.22034/cmde.2020.35546.1608.
  15. [15] Nicaise, S. and Pignotti, C. (2008), Stabilization of the wave equation with boundary or internal distributed delay, Diff. Int. Equs., 21(9-10), 935-958.