Stabilization of ternary mixtures with frictional dissipation

Article type: Research Article

Authors: Dell'Oro, Filippo | Muñoz Rivera, Jaime E.^{; ;}

Affiliations: Università di Brescia – DICATAM, Brescia, Italy. E-mail: filippo.delloro@unibs.it | National Laboratory for Scientific Computation, Rio de Janeiro, RJ, Brasil | Instituto de Matemática – UFRJ, Centro de Tecnologia, Ilha do Fundão, Cidade Universitária, Rio de Janeiro, RJ, Brasil. E-mail: rivera@lncc.br

Note: [] Corresponding author: Jaime E. Muñoz Rivera, National Laboratory for Scientific Computation, Rua Getulio Vargas 333, Quitadinha-Petrópolis 25651-070, Rio de Janeiro, RJ, Brasil. E-mail: rivera@lncc.br

Abstract: We analyze the decay properties of the solution semigroup generated by a linear evolution system modeling a mixture of three interacting continua with frictional damping. In particular, we provide conditions for the strong and exponential stability when the dissipation is contributed only by some equation of the system. Moreover, we study situations where the semigroup decays polynomially or admits trajectories with conserved energy, and we find the optimal polynomial decay rate.

Keywords: ternary mixtures, contraction semigroups, exponential decay, polynomial decay

DOI: 10.3233/ASY-141229

Journal: Asymptotic Analysis, vol. 89, no. 3-4, pp. 235-262, 2014