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Year 2020, Volume: 3 Issue: 1, 150 - 155, 15.12.2020

Erhan Pişkin , Nazlı Irkıl

Abstract

References

  • 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

Year 2020, Volume: 3 Issue: 1, 150 - 155, 15.12.2020

Erhan Pişkin , Nazlı Irkıl

Abstract

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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Keywords

Existence Blow Up p-Laplacian equation Logarithmic nonlinearity

References

  • 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).
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Erhan Pişkin

Nazlı Irkıl

Publication Date December 15, 2020
Acceptance Date October 2, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

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. December 2020;3(1):150-155.
Chicago Pişkin, Erhan, and Nazlı Irkıl. “Local Existence and Blow up for P-Laplacian Equation With Logarithmic Nonlinearity”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 150-55.
EndNote Pişkin E, Irkıl N (December 1, 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 and N. Irkıl, “Local Existence and Blow up for p-Laplacian Equation with Logarithmic Nonlinearity”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 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 (December 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 and Nazlı Irkıl. “Local Existence and Blow up for P-Laplacian Equation With Logarithmic Nonlinearity”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 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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