On global attractors for a nonlinear porous elastic system with fractional damping and memory term

• Autores: Mirelson M. Freitas, Anderson J. A. Ramos, Mauro Lima Santos, Daniel V. Rocha
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 23, Nº 4, 2022, págs. 1679-1706
• Idioma: inglés
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• Resumen

  • In this paper we study the long-time dynamics of a porous elastic system with fractional damping mechanisms acting in the first wave equation, memory term, and subjected to nonlinear source terms. Using the recent quasistability theory, we prove the existence of a smooth finite-dimensional global attractor, which is characterized as the unstable manifold of the set of stationary solutions. Moreover, the existence of exponential attractors is shown.