Limiting dynamics in one-dimensional porous-elasticity

Article type: Research Article

Authors: Freitas, M.M.^{a; *} | Santos, M.L.^b | Dos Santos, M.J.^c | Ramos, A.J.A.^a

Affiliations: [a] Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil | [b] PhD Program in Mathematics – Federal University of Pará, Augusto Corrêa Street, 01, 66075-110, Belém – PA, Brazil | [c] Federal University of Pará, Manoel de Abre Street, s/n, Faculty of Exact Sciences and Technology, 68440-000, Abaetetuba, PA, Brazil

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper we investigate the long-term behavior of the solutions of the one-dimensional porous-elasticity problem with porous dissipation and nonlinear feedback force. We prove that the porous-elasticity problem converges to a quasi-static problem for the microvoids motion as a suitable parameter J tends to zero. Finite dimensional global attractor with additional regularity in J is obtained using the recent quasi-stability theory. Finally, we compare the porous-elasticity problem with quasi-static problem, in the sense of the upper-semicontinuity of their attractors as J→0.

Keywords: Porous-elasticity, quasi-static microvoids, singular limit, global attractor, upper-semicontinuity

DOI: 10.3233/ASY-221788

Journal: Asymptotic Analysis, vol. 132, no. 1-2, pp. 153-174, 2023