Title | LARGE TIME BEHAVIOR OF MULTIDIMENSIONAL NONLINEAR LATTICES WITH NONLINEAR DAMPING |
Publication Type | Journal Article |
Year of Publication | 2010 |
Authors | OLIVEIRA, JC, PEREIRA, JM, G. MENZALA, PERLA |
Secondary Title | Communications in Applied Analysis |
Volume | 14 |
Issue | 2 |
Start Page | 155 |
Pagination | 176 |
Date Published | 04/2010 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 34D05, 34D45, 58F39. |
Abstract | In this paper we study the asymptotic behavior of solutions of multidimensional nonlinear lattices subject to cyclic boundary conditions under the effect of a nonlinear dissipation. We establish the existence of a global attractor.
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URL | http://www.acadsol.eu/en/articles/14/2/3.pdf |
Short Title | LARGE TIME BEHAVIOR OF MULTIDIMENSIONAL |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] R. V. Agarwal, Difference equations and inequalities, theory, methods and applications, Marcel Dekker, New York, Basel, 2000.
[2] P. W. Bates, K. Lu, B. Wang, Attractors for lattices dynamical systems, Internat. J. Bifur. Chaos Appl. Sci. Eng. 11 (1) (2001), 143–153. [3] W. L. Briggs, V. E. Henson, The DFT, an owners manual for the discrete Fourier Transform, SIAM, Philadelphia, 1995. [4] T. Ernaux, G. Nicolis, Propagating waves in discrete bistable reaction-diffusion systems, Phys. D 67 (1993), 237–244.
[5] S. Flach, C. R. Willis, Discrete breathers, Physics Report 295 (1998), 181–164. [6] N. I. Karachalios, A. N. Yannacopoulos, Global existence and compact attractors for the discrete nonlinear Schr ̈odinger equation, J. Differential Equations, 217 (2005), 88–123. [7] J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM, J. Appl. Math. 47 (1987), 556–572. [8] P. G. Kevrekidis, B. A. Malomed, A. R. Bishop, D. J. Frantzeskakis, Localized vortices with a semiinteger charge in nonlinear dynamical lattices, Physical Review E 65, (2001), 1–7. [9] V. V. Konotop, G. Perla Menzala, Uniform decay rates of solutions of some nonlinear lattices, Nonlinear Analysis 54 (2003), 261–278. [10] V. V. Konotop, J. E. Munoz Rivera, G. Perla Menzala, Uniform rates of decay of solutions for a nonlinear lattice with memory, Asymptotic Analysis, 38 (2004), 167–185. [11] V. V. Konotop, G. Perla Menzala, Localized solutions of a nonlinear diatomic lattice, Quarterly of Applied Mathematics, LXIII (2) (2005), 201–223. [12] B. A. Malomed, P. G. Kevrekidis, D. J. Frantzeskakis, H. E. Nistazakis, A. N. Yamacopoulos, One- and two dimensional solitons in second-harmonic-generating lattices, Physical Review E, 65, (2002), 10–12. [13] M. Nakao, Global attractors for nonlinear wave equations with nonlinear dissipative terms, J. Differential Equations, 227 (2006), 204–229. [14] J. C. Oliveira, J. M. Pereira, G. Perla Menzala, Attractors for second order lattices with nonlinear damping, Journal of Difference Equations and Applications, 14 (9) (2008), 899–921. [15] A. Perez-Munuzuri, V. Perez-Munuzuri, V. Perez-Villar, L. O. Chua, Spiral waves on a 2-d array of nonlinear circuits, IEEE Trans. Circuits Systems 40 (1993), 872–877. [16] R. Teman, Infinite dimensional dynamical systems in Mechanics and Physics, Springer-Verlag, 1988. [17] Y. Yan, Attractors and dimensions for discretization of a weakly damped Schr ̈odinger equations and a Sine-Gordon equation, Nonlinear Analysis TMA, 20 (1993), 1417–1452. [18] S. Zhou, Attractors and approximations for lattice dynamical systems, J. Differential Equations, 200 (2004), 342–368. |