Research Article
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Year 2021, Volume: 4 Issue: 2, 172 - 187, 31.07.2021
https://doi.org/10.33773/jum.956729

Abstract

References

  • M. M. Al-Gharabli, S. A. Messaoudi, The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, Journal of Mathematical Analysis and Applications, 454(2), 1114-1128, (2017).
  • Y. Chen, R. Xu, Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity, Nonlinear Analysis, 192, 111664, (2020).
  • S. M. S. Cordeiro, D.C. Pereira, J. Ferreira, C.A Raposo, Global solutions and exponential decay to a Klein--Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term. Partial Differential Equations in Applied Mathematics, 3, 100018, (2021).
  • H. Di, Y. Shang, Z. Song, Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity. Nonlinear Analysis: Real World Applications, 51, 102968, (2020).
  • P. Gorka, Logarithmic Klein-Gordon equation, Acta Physica Polonica B, 40(1), (2009).
  • X. Han, Global existence of weak solutions for a logarithmic wave equation arising from Q-ball dynamics, Bulletin of the Korean Mathematical Society, 50(1), 275-283, (2013).
  • T. Hiramatsu, M. Kawasaki, F. Takahashi, Numerical study of Q-ball formation in gravity mediation. Journal of Cosmology and Astroparticle Physics, 2010(06), 008, (2010).
  • N. Irkıl, E. Pişkin Global existence and decay of solutions for a higher-order Kirchhoff-type systems with logarithmic nonlinearities, Quaestiones Mathematicae, 1-24, (2021), (in press).
  • G. Kirchhoff, Vorlesungen über Mechanik, 3rd ed., Teubner, Leipzig, 1883.
  • W. Lian, M. S. Ahmed, R. Xu, Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity, Nonlinear Analysis, 184, 239-257, (2019).
  • G. Lin, L. Hu, The gloabal attractor for a class of higher-order coupled Kirchhoff-type equations with strong linear damping, European Journal of Mathematics and Computer Science, 4(1), 63-77, (2017).
  • A. Peyravi, Blow up solutions to a system of higher-order Kirchhoff-type equations with positive initial energy, Taiwanese Journal of Mathematics, 21(4), 767-789, (2017).
  • E. Pişkin, N.Irkıl, Well-posedness results for a sixth-order logarithmic Boussinesq equation. Filomat, 33(13), 3985-4000, (2019).
  • E. Pişkin, N.Irkıl, Blow up of the solution for hyperbolic type equation with logarithmic nonlinearity, Aligarh Bulletin of Mathematics, 39 (1-2) ,19-29, (2020).
  • E. Pişkin, N. Polat, Uniform decay and blow up of solutions for a system of nonlinear higher-order Kirchhoff-type equations with damping and source terms, Contemporary Analysis and Applied Mathematics; 1 (2), 181-199, (2011).
  • E. Pişkin, E. Harman, Energy Decay of solutions for a system of higher-order Kirchhoff type equations, Journal of New Theory, (29), 89-100, (2019).
  • X. Wang, Y.Chen, Y. Yang, J. Li, R. Xu, Kirchhoff-type system with linear weak damping and logarithmic nonlinearities, Nonlinear Analysis, 188, 475-499, (2019).
  • Y. Yang, J. Li, T. Yu, Qualitative analysis of solutions for a class of Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term, Applied Numerical Mathematics, 141, 263-285, (2019).
  • Q. Hu, H. Zhang, G. Liu, Asymptotic behavior for a class of logarithmic wave equations with linear damping, Applied Mathematics and Optimization, 79(1), 131-144, (2019).

GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES

Year 2021, Volume: 4 Issue: 2, 172 - 187, 31.07.2021
https://doi.org/10.33773/jum.956729

Abstract

This paper deals with the the system a class of nonlinear higher-order Kirchhoff-type equations with logarithmic nonlinearities. Under the appropriate assumptions, the theorem of global nonexistence is established at positive initial energy levels.

References

  • M. M. Al-Gharabli, S. A. Messaoudi, The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term, Journal of Mathematical Analysis and Applications, 454(2), 1114-1128, (2017).
  • Y. Chen, R. Xu, Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity, Nonlinear Analysis, 192, 111664, (2020).
  • S. M. S. Cordeiro, D.C. Pereira, J. Ferreira, C.A Raposo, Global solutions and exponential decay to a Klein--Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term. Partial Differential Equations in Applied Mathematics, 3, 100018, (2021).
  • H. Di, Y. Shang, Z. Song, Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity. Nonlinear Analysis: Real World Applications, 51, 102968, (2020).
  • P. Gorka, Logarithmic Klein-Gordon equation, Acta Physica Polonica B, 40(1), (2009).
  • X. Han, Global existence of weak solutions for a logarithmic wave equation arising from Q-ball dynamics, Bulletin of the Korean Mathematical Society, 50(1), 275-283, (2013).
  • T. Hiramatsu, M. Kawasaki, F. Takahashi, Numerical study of Q-ball formation in gravity mediation. Journal of Cosmology and Astroparticle Physics, 2010(06), 008, (2010).
  • N. Irkıl, E. Pişkin Global existence and decay of solutions for a higher-order Kirchhoff-type systems with logarithmic nonlinearities, Quaestiones Mathematicae, 1-24, (2021), (in press).
  • G. Kirchhoff, Vorlesungen über Mechanik, 3rd ed., Teubner, Leipzig, 1883.
  • W. Lian, M. S. Ahmed, R. Xu, Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity, Nonlinear Analysis, 184, 239-257, (2019).
  • G. Lin, L. Hu, The gloabal attractor for a class of higher-order coupled Kirchhoff-type equations with strong linear damping, European Journal of Mathematics and Computer Science, 4(1), 63-77, (2017).
  • A. Peyravi, Blow up solutions to a system of higher-order Kirchhoff-type equations with positive initial energy, Taiwanese Journal of Mathematics, 21(4), 767-789, (2017).
  • E. Pişkin, N.Irkıl, Well-posedness results for a sixth-order logarithmic Boussinesq equation. Filomat, 33(13), 3985-4000, (2019).
  • E. Pişkin, N.Irkıl, Blow up of the solution for hyperbolic type equation with logarithmic nonlinearity, Aligarh Bulletin of Mathematics, 39 (1-2) ,19-29, (2020).
  • E. Pişkin, N. Polat, Uniform decay and blow up of solutions for a system of nonlinear higher-order Kirchhoff-type equations with damping and source terms, Contemporary Analysis and Applied Mathematics; 1 (2), 181-199, (2011).
  • E. Pişkin, E. Harman, Energy Decay of solutions for a system of higher-order Kirchhoff type equations, Journal of New Theory, (29), 89-100, (2019).
  • X. Wang, Y.Chen, Y. Yang, J. Li, R. Xu, Kirchhoff-type system with linear weak damping and logarithmic nonlinearities, Nonlinear Analysis, 188, 475-499, (2019).
  • Y. Yang, J. Li, T. Yu, Qualitative analysis of solutions for a class of Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term, Applied Numerical Mathematics, 141, 263-285, (2019).
  • Q. Hu, H. Zhang, G. Liu, Asymptotic behavior for a class of logarithmic wave equations with linear damping, Applied Mathematics and Optimization, 79(1), 131-144, (2019).
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Nazlı Irkıl 0000-0002-9130-2893

Erhan Pişkin 0000-0001-6587-4479

Publication Date July 31, 2021
Submission Date June 23, 2021
Acceptance Date July 29, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Irkıl, N., & Pişkin, E. (2021). GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES. Journal of Universal Mathematics, 4(2), 172-187. https://doi.org/10.33773/jum.956729
AMA Irkıl N, Pişkin E. GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES. JUM. July 2021;4(2):172-187. doi:10.33773/jum.956729
Chicago Irkıl, Nazlı, and Erhan Pişkin. “GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES”. Journal of Universal Mathematics 4, no. 2 (July 2021): 172-87. https://doi.org/10.33773/jum.956729.
EndNote Irkıl N, Pişkin E (July 1, 2021) GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES. Journal of Universal Mathematics 4 2 172–187.
IEEE N. Irkıl and E. Pişkin, “GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES”, JUM, vol. 4, no. 2, pp. 172–187, 2021, doi: 10.33773/jum.956729.
ISNAD Irkıl, Nazlı - Pişkin, Erhan. “GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES”. Journal of Universal Mathematics 4/2 (July 2021), 172-187. https://doi.org/10.33773/jum.956729.
JAMA Irkıl N, Pişkin E. GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES. JUM. 2021;4:172–187.
MLA Irkıl, Nazlı and Erhan Pişkin. “GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES”. Journal of Universal Mathematics, vol. 4, no. 2, 2021, pp. 172-87, doi:10.33773/jum.956729.
Vancouver Irkıl N, Pişkin E. GLOBAL NONEXISTENCE OF THE HIGHER ORDER KIRCHHOFF TYPE SYSTEM WITH LOGARITHMIC NONLINEARITIES. JUM. 2021;4(2):172-87.