On the uniqueness and analyticity in viscoelasticity with double porosity

Article type: Research Article

Authors: Bazarra, N.^a | Fernández, J.R.^a | Leseduarte, M.C.^b | Magaña, A.^{b; *} | Quintanilla, R.^b

Affiliations: [a] Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain | [b] Departament de Matemàtiques, Universitat Politècnica de Catalunya, Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa, C. Colom 11, 08222 Terrassa, Barcelona, Spain

Correspondence: [*] Corresponding author. Tel.: +34 937 398 206; E-mail: antonio.magana@upc.edu.

Abstract: In this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained.

Keywords: Viscoelasticity, double porosity, uniqueness, analyticity, exponential decay

DOI: 10.3233/ASY-181500

Journal: Asymptotic Analysis, vol. 112, no. 3-4, pp. 151-164, 2019