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Long time dynamics of a multidimensional nonlinear lattice with memory

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  • This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction on the nonlinear term we obtain decay rates of the total energy. These rates could be exponential, polynomial or several other intermediate types.
    Mathematics Subject Classification: Primary: 34D45, 34D05; Secondary: 39A12.


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