JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERAL DECAY FOR A SEMILINEAR WAVE EQUATION WITH BOUNDARY FRICTIONAL AND MEMORY CONDITIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GENERAL DECAY FOR A SEMILINEAR WAVE EQUATION WITH BOUNDARY FRICTIONAL AND MEMORY CONDITIONS
Park, Sun Hye;
  PDF(new window)
 Abstract
In this paper, we investigate the influence of boundary dissipations on decay property of the solutions for a semilinear wave equation with damping and memory condition on the boundary using the multiplier technique.
 Keywords
wave equation;boundary damping;memory condition;general decay rate;Lyapunov functional;
 Language
English
 Cited by
1.
Existence and general decay for nondissipative distributed systems with boundary frictional and memory dampings and acoustic boundary conditions, Zeitschrift für angewandte Mathematik und Physik, 2015, 66, 4, 1595  crossref(new windwow)
2.
Existence and general decay for nondissipative hyperbolic differential inclusions with acoustic/memory boundary conditions, Mathematische Nachrichten, 2016, 289, 2-3, 300  crossref(new windwow)
3.
Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type, Journal of Dynamical and Control Systems, 2017, 23, 2, 237  crossref(new windwow)
 References
1.
M. Aassila, M. M. Cavalcanti, and J. A. Soriano, Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain, SIAM J. Control Optim. 38 (2000), no. 5, 1581-1602. crossref(new window)

2.
F. Alabau-Boussouira, Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems, Appl. Math. Optim. 51 (2005), no. 1, 61-105. crossref(new window)

3.
M. M. Cavalcanti, V. N. Domingos Cavalcanti, and P. Martinez, General decay rate estimates for viscoelastic dissipative systems, Nonlinear Anal. 68 (2008), no. 1, 177-193. crossref(new window)

4.
M. M. Cavalcanti and A. Guesmia, General decay rates of solutions to a nonlinear wave equation with boundary conditions of memory type, Differential Integral Equations 18 (2005), no. 5, 583-600.

5.
A. Guesmia, A new approach of stabilization of nondissipative distributed systems, SIAM J. Control Optim. 42 (2003), no. 1, 24-52. crossref(new window)

6.
A. Guesmia and S. A. Messaoudi, General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping, Math. Methods Appl. Sci. 32 (2009), no. 16, 2102-2122. crossref(new window)

7.
V. Komornik, Exact Controllability and Stabilization: The Multiplier Method, John Wiley and Sons, Masson, 1994.

8.
V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. (9) 69 (1990), no. 1, 33-54.

9.
I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Differential Integral Equations 6 (1993), no. 3, 507-533.

10.
P. Martinez, A new method to obtain decay rate estimates for dissipative systems, ESAIM Control Optim. Calc. Var. 4 (1999), 419-444. crossref(new window)

11.
S. A. Messaoudi, General decay of solutions of a viscoelastic equation, J. Math. Anal. Appl. 341 (2008), no. 2, 1457-1467. crossref(new window)

12.
S. A. Messaoudi and A. Soufyane, General decay of solutions of a wave equation with a boundary control of memory type, Nonlinear Anal. R.W.A. 11 (2010), no. 4, 2896-2904. crossref(new window)

13.
J. Y. Park and S. H. Park, On solutions for a hyperbolic system with differential inclusion and memory source term on the boundary, Nonlinear Anal. 57 (2004), no. 3, 459-472. crossref(new window)

14.
S. H. Park, J. Y. Park, and J. M. Jeong, Boundary stabilization of hyperbolic hemivariational inequalities, Acta Appl. Math. 104 (2008), no. 2, 139-150. crossref(new window)

15.
R. Triggiani, Wave equation on a bounded domain with boundary dissipation: An operator approach, J. Math. Anal. Appl. 137 (1989), no. 2, 438-461.

16.
E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback, SIAM J. Control Optim. 28 (1990), no. 2, 466-477. crossref(new window)