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

IJARM > Volume 6 > On Behaviors of the Energy of Solutions for Some...
< Back to Volume

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

Full Text PDF


In this paper we are concerned with nonlinear damped hyperbolic equation with p-Laplace of the form uttpu+ σ(t)(utut)+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.


International Journal of Advanced Research in Mathematics (Volume 6)
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:
Sep 2016

[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