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.
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
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.
.
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.
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).
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.