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<p>This work investigates the asymptotic behavior of the solutions of a lattice dynamical system based on a binary mixture-type system. First, we prove the existence and uniqueness of solutions. Next, we show that the semigroup generated by solutions of the system is dissipative i.e., there exists a bounded absorbing set that attracts every bounded set, and satisfies the “asymptotic tail estimate” property. This property allows the asymptotic compactness of the semigroup to be established, resulting in the existence of a global attractor. Finally, we obtain approximations of the global attractor through global attractors of finite-dimensional approximate systems.</p>

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Lattice dynamics for a nonlinear binary mixture of solids system

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Manoel J. Dos Santos,
  • Joao C. P. Fortes,
  • Alan C. B. Dos Santos

摘要

This work investigates the asymptotic behavior of the solutions of a lattice dynamical system based on a binary mixture-type system. First, we prove the existence and uniqueness of solutions. Next, we show that the semigroup generated by solutions of the system is dissipative i.e., there exists a bounded absorbing set that attracts every bounded set, and satisfies the “asymptotic tail estimate” property. This property allows the asymptotic compactness of the semigroup to be established, resulting in the existence of a global attractor. Finally, we obtain approximations of the global attractor through global attractors of finite-dimensional approximate systems.