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Yıl 2021, Cilt: 9 Sayı: 2, 238 - 244, 15.10.2021

Hazal Yüksekkaya Erhan Pişkin

Öz

Kaynakça

  • 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

Yıl 2021, Cilt: 9 Sayı: 2, 238 - 244, 15.10.2021

Hazal Yüksekkaya Erhan Pişkin

Öz

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.

Anahtar Kelimeler

Decay term logarithmic source term m-Laplacian equation nonexistence of solutions

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Hazal Yüksekkaya

Erhan Pişkin

Yayımlanma Tarihi 15 Ekim 2021
Gönderilme Tarihi 9 Mart 2021
Kabul Tarihi 26 Ağustos 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 2

Kaynak Göster

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.
AMA Yüksekkaya H, Pişkin E. Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp J. Math. Ekim 2021;9(2):238-244.
Chicago Yüksekkaya, Hazal, ve Erhan Pişkin. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics 9, sy. 2 (Ekim 2021): 238-44.
EndNote Yüksekkaya H, Pişkin E (01 Ekim 2021) Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp Journal of Mathematics 9 2 238–244.
IEEE H. Yüksekkaya ve E. Pişkin, “Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term”, Konuralp J. Math., c. 9, sy. 2, ss. 238–244, 2021.
ISNAD Yüksekkaya, Hazal - Pişkin, Erhan. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics 9/2 (Ekim 2021), 238-244.
JAMA 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 ve Erhan Pişkin. “Nonexistence of Solutions for a Logarithmic M-Laplacian Type Equation With Delay Term”. Konuralp Journal of Mathematics, c. 9, sy. 2, 2021, ss. 238-44.
Vancouver Yüksekkaya H, Pişkin E. Nonexistence of Solutions for a Logarithmic m-Laplacian Type Equation with Delay Term. Konuralp J. Math. 2021;9(2):238-44.
 Kapak Resmi İndir
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