Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IJARM > IJARM Volume 6 > On Behaviors of the Energy of Solutions for Some...
On Behaviors of the Energy of Solutions for Some Damped Nonlinear Hyperbolic Equations with <i>p</i>-Laplacian
< Back to Volume

On Behaviors of the Energy of Solutions for Some Damped Nonlinear Hyperbolic Equations with p-Laplacian

Full Text PDF

Abstract:

In this paper we are concerned with nonlinear damped hyperbolic equation with p-Laplace of the form utt-Δpu+ σ(t)(ut-Δut)+w|u|m-2u = |u|r-2u. Used the multiplier techniques combined with a nonlinear integral inequalities given by Martinez we established a decay rate estimate for the energy.

Info:

Periodical:
International Journal of Advanced Research in Mathematics (Volume 6)
Pages:
13-20
DOI:
https://doi.org/10.18052/www.scipress.com/IJARM.6.13
Citation:
S. Mokeddem, "On Behaviors of the Energy of Solutions for Some Damped Nonlinear Hyperbolic Equations with p-Laplacian", International Journal of Advanced Research in Mathematics, Vol. 6, pp. 13-20, 2016
Online since:
September 2016
Authors:
Soufiane Mokeddem
Keywords:
Decay Estimate of Energy, Hyperbolic Equations with p-Laplace
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] N. Amroun, S. Mimouni, Asymptotic behaviour of solutions for some weakly dissipative wave equations of p-Laplacian type, Applied Mathematics E-Notes. 11 (2011) 175-183.

[2] A. Benaissa, S. A. Messaoudi, Exponential decay of solutions of a nonlinearly damped wave equation, Nonlinear Differ. Equ. Appl. 12(4) (2005) 391-399.

[3] A. Benaissa, S. Mokeddem, Decay estimates for the wave equation of p-Laplacian type with dissipation of m-Laplacian type, Math. Methods Appl. Sci. 30(2) (2007) 237-247.

[4] C. Chen, H. Yao, L. Shao, Global Existence, Uniqueness, and Asymptotic behavior of solution for p-Laplacian Type wave equation. J. Inequal. Appl. 2010, Art. ID 216760.

[5] H. Gao, T. F. Ma, Global solutions for a nonlinear wave equation with the p-Laplacian operator, Electronic Journal of Qualitative Theory of Differential Equations. 11 (1999) 1-13.

[6] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, DunodGauthier Villars, Paris, France, (1969).

[7] T. F. Ma, J. A. Soriano, On weak solutions for an evolution equation with exponential nonlinearities, Nonlinear Anal. 37(8) (1999) 1029-1038.

[8] P. Martinez, A new method to decay rate estimates for dissipative systems, ESAIM Control Optim. Calc. Var. 4 (1999) 419-444.

[9] S. Mokeddem, Kh. B. W. Mansour, Asymptotic behaviour of solutions for p-Laplacian wave equation with m-Laplacian dissipation, Z. Anal. Anwend. 33(3) (2014) 259-269.

[10] M. I. Mustafa, A. S. Messaoudi, General energy decay rates for a weakly damped wave equation, Commun. Math. Anal. 9(2) (2010) 67-76.

[11] M. Nakao, A difference inequality and its applications to nonlinear evolution equations, Journal of the Mathematical Society of Japan. 30(4) (1978) 747-762.

[12] D. H. Sattinger, On global solution of nonlinear hyperbolic equations, Arch. Ration. Mech. Anal. 30 (1968) 148-172.

[13] Z. Yang, Existence and asymptotic behaviour of solutions for a class of quasilinear evolution equations with nonlinear damping and source terms, Mathematical Methods in the Applied Sciences. 25(10) (2002) 795-814.

[14] Y. Ye, Existence of global solutions for some nonlinear hyperbolic equation with a nonlinear dissipative term, Journal of Zhengzhou University. 29(3) (1997) 18-23.

[15] Y. Ye, On the decay of solutions for some nonlinear dissipative hyperbolic equations, Acta Mathematicae Applicatae Sinica. English Series. 20(1) (2004) 93-100.

[16] Y. Ye, Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation, Adv. Difference Equ. (2010) Article ID 357404.

[17] Y. Ye, Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation, J. Inequal. Appl. (2010) Article ID 895121.

[18] E. Zuazua, Exponential decay for the semilinear wave equation with locally dis-tributed damping, Comm. Partial Differential Equations. 15 (1990) 205-235.

[19] E. Zuazua, Uniform Stabilization of the wave equation by nonlinear boundary feed-back, SIAM J. Control Optim. 28(2) (1990) 466-477.

Show More Hide
Cited By:
This article has no citations.