Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture

• Published in: Acta mechanica Vol. 219; no. 1-2; pp. 145 - 167
• Main Authors: Alves, Margareth S., Rivera, Jaime E. Muñoz, Sepúlveda, Mauricio, Vera, Octavio
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.06.2011; Springer; Springer Nature B.V
• Subjects: Analysis; Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Materials science; Mechanical engineering; Physics; Porosity; Solid Mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Temperature; Theoretical and Applied Mechanics; Vibration; Exponential Stability; Porosity; Linear Theory; Initial Boundary; Discrete Fourier Transform; Viscoelasticity; Stabilization; Initial value problem; Mixture theory; Semigroup; Exponential stability; Porous material; Modeling; Boundary value problem; Kelvin voigt model; Homogeneous mixtures; Asymptotic approximation
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-010-0443-1

In this paper, we investigate the asymptotic behavior of solutions to the initial boundary value problem for the interaction between the temperature field and the porosity fields in a homogeneous and isotropic mixture from the linear theory of porous Kelvin–Voigt materials. Our main result is to establish conditions which insure the analyticity and the exponential stability of the corresponding semigroup. We show that under certain conditions for the coefficients we obtain a lack of exponential stability. A numerical scheme is given.