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Long-Time Behavior for Second Order Lattice Dynamical Systems

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Abstract

Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l 2×l 2. For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on ℝm,m≥1.

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Authors and Affiliations

  1. Department of Mathematics, University of Jordan, Amman, 11942, Jordan

    Ahmed Y. Abdallah

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  1. Ahmed Y. Abdallah
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Correspondence to Ahmed Y. Abdallah.

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Abdallah, A.Y. Long-Time Behavior for Second Order Lattice Dynamical Systems. Acta Appl Math 106, 47–59 (2009). https://doi.org/10.1007/s10440-008-9281-8

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