Research Article
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Year 2021, Volume: 9 Issue: 2, 238 - 244, 15.10.2021
https://izlik.org/JA45XY87CL

Abstract

References

  • K. Bartkowski, P. Gorka, One dimensional Klein-Gordon equation with logarithmic nonlinearities, J. Phys. A 41 (2008).
  • I. Bialynicki-Birula, J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 23(4) (1975) 461-466.
  • I. Bialynicki-Birula, J. Mycielski, Nonlinear wave mechanics, Ann. Physics, 100(1-2) (1976) 62-93.
  • T. Cazenave, A. Haraux, Equations d'evolution avec non-linearite logarithmique, Ann. Fac. Sci. Toulouse Math., 2(1) (1980) 21-51.
  • R. Datko, J. Lagnese, M. P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim., 24(1) (1986) 152-156.
  • P. Gorka, Logarithmic Klein-Gordon equation, Acta Phys. Polon. B 40 (2009) 59--66.
  • M. Kafini, S. A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13 (2016) 237-247. M. Kafini, S. Messaoudi, Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Appl. Anal., (2018) 1-18.
  • C.N. Le, X. T. Le, Global solution and blow up for a class of Pseudo p-Laplacian evolution equations with logarithmic nonlinearity, Comput. Math. Appl., 73(9) (2017) 2076.
  • N. Mezouar, S.M. Boulaaras, A. Allahem, Global existence of solutions for the viscoelastic Kirchhoff equation with logarithmic source terms, J. Complex, (2020), 1-25. S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21 (2008) 935-958.
  • S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim., 45(5) (2006) 1561-1585.
  • S.H. Park, Global existence, energy decay and blow-up of solutions for wave equations with time delay and logariithmic source, Adv. Differ. Equ., 2020:631 (2020) 1-17.
  • E. Pişkin, N. Irkıl, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. & Nat. Sci., 10(2) (2019) 213-220.
  • E. Pişkin, H. Yüksekkaya, Nonexistence of solutions of a delayed wave equation with variable-exponents, C-POST, 3(1), 97--101, 2020. E. Pişkin, H. Yüksekkaya, Decay and blow up of solutions for a delayed wave equation with variable-exponents, C-POST, 3(1), 91--96, 2020.
  • E. Pişkin, H. Yüksekkaya, Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 1-14, 2020, doi:10.22034/cmde.2020.35546.1608. (In press)
  • E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, 1-19. (Accepted)
  • E. Pişkin, H. Yüksekkaya, Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term, J. Math. Anal., 12(1), 56-64, 2021.

Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term

Year 2021, Volume: 9 Issue: 2, 238 - 244, 15.10.2021
https://izlik.org/JA45XY87CL

Abstract

In this work, we consider a logarithmic m-Laplacian type equation with delay term with initial and boundary conditions. Under suitable conditions on the initial data, we study the nonexistence of solutions in a finite time with negative initial energy $E\left( 0\right) <0$ in a bounded domain.

References

  • K. Bartkowski, P. Gorka, One dimensional Klein-Gordon equation with logarithmic nonlinearities, J. Phys. A 41 (2008).
  • I. Bialynicki-Birula, J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 23(4) (1975) 461-466.
  • I. Bialynicki-Birula, J. Mycielski, Nonlinear wave mechanics, Ann. Physics, 100(1-2) (1976) 62-93.
  • T. Cazenave, A. Haraux, Equations d'evolution avec non-linearite logarithmique, Ann. Fac. Sci. Toulouse Math., 2(1) (1980) 21-51.
  • R. Datko, J. Lagnese, M. P. Polis, An example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM J. Control Optim., 24(1) (1986) 152-156.
  • P. Gorka, Logarithmic Klein-Gordon equation, Acta Phys. Polon. B 40 (2009) 59--66.
  • M. Kafini, S. A. Messaoudi, A blow-up result in a nonlinear wave equation with delay, Mediterr. J. Math., 13 (2016) 237-247. M. Kafini, S. Messaoudi, Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay, Appl. Anal., (2018) 1-18.
  • C.N. Le, X. T. Le, Global solution and blow up for a class of Pseudo p-Laplacian evolution equations with logarithmic nonlinearity, Comput. Math. Appl., 73(9) (2017) 2076.
  • N. Mezouar, S.M. Boulaaras, A. Allahem, Global existence of solutions for the viscoelastic Kirchhoff equation with logarithmic source terms, J. Complex, (2020), 1-25. S. Nicaise, C. Pignotti, Stabilization of the wave equation with boundary or internal distributed delay, Differ. Integral Equ., 21 (2008) 935-958.
  • S. Nicaise, C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim., 45(5) (2006) 1561-1585.
  • S.H. Park, Global existence, energy decay and blow-up of solutions for wave equations with time delay and logariithmic source, Adv. Differ. Equ., 2020:631 (2020) 1-17.
  • E. Pişkin, N. Irkıl, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. & Nat. Sci., 10(2) (2019) 213-220.
  • E. Pişkin, H. Yüksekkaya, Nonexistence of solutions of a delayed wave equation with variable-exponents, C-POST, 3(1), 97--101, 2020. E. Pişkin, H. Yüksekkaya, Decay and blow up of solutions for a delayed wave equation with variable-exponents, C-POST, 3(1), 91--96, 2020.
  • E. Pişkin, H. Yüksekkaya, Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay, Comput. Methods Differ. Equ., 1-14, 2020, doi:10.22034/cmde.2020.35546.1608. (In press)
  • E. Pişkin, H. Yüksekkaya, Nonexistence of global solutions of a delayed wave equation with variable-exponents, Miskolc Math. Notes, 1-19. (Accepted)
  • E. Pişkin, H. Yüksekkaya, Blow-up of solutions for a logarithmic quasilinear hyperbolic equation with delay term, J. Math. Anal., 12(1), 56-64, 2021.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Hazal Yüksekkaya

Erhan Pişkin

Submission Date March 9, 2021
Acceptance Date August 26, 2021
Publication Date October 15, 2021
IZ https://izlik.org/JA45XY87CL
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Yüksekkaya, H., & Pişkin, E. (2021). Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp Journal of Mathematics, 9(2), 238-244. https://izlik.org/JA45XY87CL
AMA 1.Yüksekkaya H, Pişkin E. Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp J. Math. 2021;9(2):238-244. https://izlik.org/JA45XY87CL
Chicago Yüksekkaya, Hazal, and Erhan Pişkin. 2021. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics 9 (2): 238-44. https://izlik.org/JA45XY87CL.
EndNote Yüksekkaya H, Pişkin E (October 1, 2021) Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp Journal of Mathematics 9 2 238–244.
IEEE [1]H. Yüksekkaya and E. Pişkin, “Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term”, Konuralp J. Math., vol. 9, no. 2, pp. 238–244, Oct. 2021, [Online]. Available: https://izlik.org/JA45XY87CL
ISNAD Yüksekkaya, Hazal - Pişkin, Erhan. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics 9/2 (October 1, 2021): 238-244. https://izlik.org/JA45XY87CL.
JAMA 1.Yüksekkaya H, Pişkin E. Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp J. Math. 2021;9:238–244.
MLA Yüksekkaya, Hazal, and Erhan Pişkin. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics, vol. 9, no. 2, Oct. 2021, pp. 238-44, https://izlik.org/JA45XY87CL.
Vancouver 1.Yüksekkaya H, Pişkin E. Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp J. Math. [Internet]. 2021 Oct. 1;9(2):238-44. Available from: https://izlik.org/JA45XY87CL
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