Soufiane Mokeddem


In this paper we shall investigate the decay properties of energy of p-Laplacian wave equation with strong damping. We first investigate the global existence by constructing a stable set in . After that we show the asymptotic behavior of global solutions through the use multiplier method combined with some integral inequalities due to Komornik.

Full Text:



D. Ang and A. Dinh, Strong solutions of quasilinear wave equation with nonlinear damping. Siam Journal on Mathematical Analysis. 19 (1988), 289–299.

A. Benaissa and S. Mimouni, Energy decay of solutions of wave equation of p-Laplacian type with a weakly nonlinear dissipation, JIPAM. J. Inequal. Pure Appl. Math. 7 (2006)-1, Article 15, 8 pp.

C. Chen, H. Yao and L. Shao, Global Existence, Uniqueness, and Asymptotic behavior of solution for p-Laplacian Type wave equation. J. Inequal. Appl. 2010, Art. ID 216760, 15 pp.

A. Haraux, Oscillations forcées pour certains systèmes dissipatifs nonlinéaires. Preprint No.78010, Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1978.

A. Haraux, Semi-groupes linéaires et équations d’évolution linéaires périodiques. Preprint No. 78011, Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1978.

V. Komornik, Exact Controllability and Stabilization. RAM: Research in Applied Mathematics. Masson, Paris; Jhons Wiley, Ltd, Chichester. 1994.

V. Komornik, Decay estimates for the wave equation with internal damping. International Series of Num. Math. Birkh¨auser Verlag Basel. 118 (1994), 253–266.

J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires. Dunod-Gauthier Villars. Paris, France, 1969.

T. F. Ma and J. A. Soriano, On weak solutions for an evolution equation with exponential nonlinearities, Nonlinear Analysis: Theory, Methods and Applications. 37 (1999), No. 8, 1029-1038.

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

S. Mokeddem and Kh. B. W. Mansour, Asymptotic behaviour of solutions for p-Laplacian wave equation with m-Laplacian dissipation, Z. Anal. Anwend. vol. 33, no. 3, pp. 259 – 269, 2014.

S. Mokeddem and Kh. B. W. Mansour, The Rate at Which the Energy of Solutions for a Class of p-Laplacian Wave Equation Decays, International Journal of Differential Equations, vol. 2015, Article ID 721503, 5 pages, 2015.

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

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

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 (2002), 795–814.

Y. J. Ye, On the decay of solutions for some nonlinear dissipative hyperbolic equations, Acta Mathematicae Applicatae Sinica. English Series. 20 (2004), 93–100.

Y. J. Ye, Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation, Adv. Difference Equ. 2010, Art. ID 357404, 12 pp.

Y. J. Ye, Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation, J. Inequal. Appl. 2010, Art. ID 895121, 10 pp.


  • There are currently no refbacks.

MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
ISSN 2371-6193