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Yıl 2020, Cilt: 3 Sayı: 1, 150 - 155, 15.12.2020

Erhan Pişkin , Nazlı Irkıl

Öz

Kaynakça

  • 1 M. M. Al-Gharabli, S. A. Messaoudi, Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, J. Evol. Equ., 18(1), (2018), 105-125.
  • 2 I. Bialynicki-Birula, J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 23(4) (1975), 461-466.
  • 3 Y. Cao, C. Liu, Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity, Electron. J. Differ. Equ, 116 (2018), 1-19.
  • 4 T. Cazenave, A. Haraux, Equations d’evolution avec non linéarité logarithmique, Ann. Fac. Sci. Toulouse, 2(1) (1980), 21-51.
  • 5 H. Chen, S. Y. Tian, Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, J. Differ. Equ., 258 (2015), 4424-4442.
  • 6 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 Anal., (2020), Article ID 111664,39 pages.
  • 7 P. Gorka, Logarithmic Klein–Gordon equation, Acta Phys. Polon., 40(1) (2009), 59–66.
  • 8 C. Liu, Y. Ma, Blow up for a fourth order hyperbolic equation with the logarithmic nonlinearity, Appl. Math. Lett., 98 (2019), 1-6.
  • 9 M. Kafini, S. Messaoudi, Local existence and blow up of slutions to a logarithmic nonlinear wave equation with delay, Appl. Anal.,99(3) (2020), 530-547.
  • 10 E. Pi¸skin, Sobolev Spaces, Seçkin Publishing, (2017). (in Turkish).
  • 11 E. Pi¸skin , N. Irkıl, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. and Nat. Sci., 10(2) (2019), 213-220.
  • 12 R. Xu, W. Lian, X. Kong, Y. Yang, Fourth order wave equation with nonlinear strain and logarithmic nonlinearity, Appl. Numer. Math., 141 (2019), 185-205.
  • 13 Y. Ye, Logarithmic viscoelastic wave equation in three-dimensional space, Appl. Anal., (in press).

Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity

Yıl 2020, Cilt: 3 Sayı: 1, 150 - 155, 15.12.2020

Erhan Pişkin , Nazlı Irkıl

Öz

This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term.
By the contraction mapping criterion and following the proof lines in [15], we establish the local existence of weak solutions. Finally, under suitable conditions, we present the finite-time blow up of solutions for negative initial energy.
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Anahtar Kelimeler

Existence Blow Up p-Laplacian equation Logarithmic nonlinearity

Kaynakça

  • 1 M. M. Al-Gharabli, S. A. Messaoudi, Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term, J. Evol. Equ., 18(1), (2018), 105-125.
  • 2 I. Bialynicki-Birula, J. Mycielski, Wave equations with logarithmic nonlinearities, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 23(4) (1975), 461-466.
  • 3 Y. Cao, C. Liu, Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity, Electron. J. Differ. Equ, 116 (2018), 1-19.
  • 4 T. Cazenave, A. Haraux, Equations d’evolution avec non linéarité logarithmique, Ann. Fac. Sci. Toulouse, 2(1) (1980), 21-51.
  • 5 H. Chen, S. Y. Tian, Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity, J. Differ. Equ., 258 (2015), 4424-4442.
  • 6 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 Anal., (2020), Article ID 111664,39 pages.
  • 7 P. Gorka, Logarithmic Klein–Gordon equation, Acta Phys. Polon., 40(1) (2009), 59–66.
  • 8 C. Liu, Y. Ma, Blow up for a fourth order hyperbolic equation with the logarithmic nonlinearity, Appl. Math. Lett., 98 (2019), 1-6.
  • 9 M. Kafini, S. Messaoudi, Local existence and blow up of slutions to a logarithmic nonlinear wave equation with delay, Appl. Anal.,99(3) (2020), 530-547.
  • 10 E. Pi¸skin, Sobolev Spaces, Seçkin Publishing, (2017). (in Turkish).
  • 11 E. Pi¸skin , N. Irkıl, Mathematical behavior of solutions of p-Laplacian equation with logarithmic source term, Sigma J. Eng. and Nat. Sci., 10(2) (2019), 213-220.
  • 12 R. Xu, W. Lian, X. Kong, Y. Yang, Fourth order wave equation with nonlinear strain and logarithmic nonlinearity, Appl. Numer. Math., 141 (2019), 185-205.
  • 13 Y. Ye, Logarithmic viscoelastic wave equation in three-dimensional space, Appl. Anal., (in press).
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan Pişkin

Nazlı Irkıl

Yayımlanma Tarihi 15 Aralık 2020
Kabul Tarihi 2 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Pişkin, E., & Irkıl, N. (2020). Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity. Conference Proceedings of Science and Technology, 3(1), 150-155.
AMA Pişkin E, Irkıl N. Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity. Conference Proceedings of Science and Technology. Aralık 2020;3(1):150-155.
Chicago Pişkin, Erhan, ve Nazlı Irkıl. “Local Existence and Blow up for P-Laplacian Equation With Logarithmic Nonlinearity”. Conference Proceedings of Science and Technology 3, sy. 1 (Aralık 2020): 150-55.
EndNote Pişkin E, Irkıl N (01 Aralık 2020) Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity. Conference Proceedings of Science and Technology 3 1 150–155.
IEEE E. Pişkin ve N. Irkıl, “Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity”, Conference Proceedings of Science and Technology, c. 3, sy. 1, ss. 150–155, 2020.
ISNAD Pişkin, Erhan - Irkıl, Nazlı. “Local Existence and Blow up for P-Laplacian Equation With Logarithmic Nonlinearity”. Conference Proceedings of Science and Technology 3/1 (Aralık 2020), 150-155.
JAMA Pişkin E, Irkıl N. Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity. Conference Proceedings of Science and Technology. 2020;3:150–155.
MLA Pişkin, Erhan ve Nazlı Irkıl. “Local Existence and Blow up for P-Laplacian Equation With Logarithmic Nonlinearity”. Conference Proceedings of Science and Technology, c. 3, sy. 1, 2020, ss. 150-5.
Vancouver Pişkin E, Irkıl N. Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity. Conference Proceedings of Science and Technology. 2020;3(1):150-5.
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