Kyungpook Mathematical Journal

  • 제61권1호
  • /
  • Pages.1-10
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  • 2021
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Blow-up of Solutions for Higher-order Nonlinear Kirchhoff-type Equation with Degenerate Damping and Source

  • 투고 : 2020.11.01
  • 심사 : 2020.12.14
  • 발행 : 2021.03.31
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초록

This paper is concerned the finite time blow-up of solution for higher-order nonlinear Kirchhoff-type equation with a degenerate term and a source term. By an appropriate Lyapunov inequality, we prove the finite time blow-up of solution for equation (1.1) as a suitable conditions and the initial data satisfying ||Dmu0|| > B-(p+2)/(p-2q), E(0) < E1.

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참고문헌

  1. V. Barbu, I. Lasiecka and M. A. Rammaha, On nonlinear wave equations with degenerate damping and source terms, Trans. Amer. Math. Soc., 357(7)(2005), 2571-2611. https://doi.org/10.1090/S0002-9947-05-03880-8
  2. Y. Boukhatem and B. Benabderrahmane, Existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions, Nonlinear Anal., 97(2014), 191-209. https://doi.org/10.1016/j.na.2013.11.019
  3. Y. Boukhatem and B. Benabderrahmane, Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions, Acta Math. Sin., 32(2)(2016), 153-174. https://doi.org/10.1007/s10114-016-5093-3
  4. X. Han and M. Wang, Global existence and blow-up of solutions for nonlinear viscoelastic wave equation with degenerate damping and source, Math. Nachr., 284(5-6)(2011), 703-716. https://doi.org/10.1002/mana.200810168
  5. J. M. Jeong, J. Y. Park and Y. H. Kang, Energy decay rates for viscoelastic wave equation with dynamic boundary conditions, J. Comput. Anal. Appl., 19(3)(2015), 500-517.
  6. J. M. Jeong, J. Y. Park and Y. H. Kang, Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions, Bound. Value Probl., (2017), Paper No. 42, 10 pp.
  7. J. M. Jeong, J. Y. Park and Y. H. Kang, Global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions, Comput. Math. Appl., 76(2018), 661-671. https://doi.org/10.1016/j.camwa.2018.05.006
  8. Y. H. Kang, J. Y. Park and D. Kim, A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions, Bound. Value Probl., (2018), Paper No. 139, 19 pp.
  9. S. Kim, J. Y. Park and Y. H. Kang, Stochastic quasilinear viscoelastic wave equation with degenerate damping and source terms, Comput. Math. Appl., 75(2018), 3987-3994. https://doi.org/10.1016/j.camwa.2018.03.008
  10. S. Kim, J. Y. Park and Y. H. Kang, Stochastic quasilinear viscoelastic wave equation with nonlinear damping and source terms, Bound. Value Probl., (2018), Paper No. 14, 15 pp.
  11. M. Kirane and B. Said-Houari, Existence and asymptotic stability of a viscoelastic wave equation with a delay, Z. Angew. Math. Phys., 62(2011), 1065-1082. https://doi.org/10.1007/s00033-011-0145-0
  12. F. Li, Global existence and blow-up of solutions for a higher-order Kirchhoff-type equation with nonlinear dissipation, Appl. Math. Lett, 17(2004), 1409-1414. https://doi.org/10.1016/j.am1.2003.07.014
  13. W. Liu and M. Wang, Global nonexistence of solutions with positive initial energy for a class of wave equations, Math. Methods Appl. Sci., 32(2009), 594-605. https://doi.org/10.1002/mma.1054
  14. S. A. Messaoudi and B. S. Houari, A blow-up result for a higher-order nonlinear Kirchhoff-type hyperbolic equation, Appl. Math. Lett., 20(2007), 866-871. https://doi.org/10.1016/j.aml.2006.08.018
  15. E. Piskin, On the decay and blow up of solutions for a quasilinear hyperbolic equations with nonlinear damping and source terms, Bound. Value Probl., (2015), 2015:127, 14 pp.
  16. F. Q. Sun and M. Wang, Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms, Nonlinear Anal., 64(2006), 739-761. https://doi.org/10.1016/j.na.2005.04.050
  17. S. T. Wu, Non-existence of global solutions for a class of wave equations with nonlinear damping and source terms, Proc. Roy. Soc. Edinburgh Sect. A, 141(4)(2011), 865-880. https://doi.org/10.1017/S0308210510001125