The lack of polynomial stability to mixtures with memory

Leonardo Henry Alejandro Aguilar; Jaime Edilberto Muñoz Rivera; Pedro Gamboa Romero

doi:10.5269/bspm.47878

Leonardo Henry Alejandro Aguilar Universidad Nacional Agr´aria La Molina http://orcid.org/0000-0001-5354-4325
Jaime Edilberto Muñoz Rivera Universidade Federal do Rio de Janeiro
Pedro Gamboa Romero Universidade Federal do Rio de Janeiro

Résumé

We consider the system modeling a mixture of n materials with memory. We show that the corresponding semigroup is exponentially stable if and only if the imaginary axis is contained in the resolvent set of the innitesimal generator. In particular this implies the lack of polynomial stability to the corresponding semigroup.

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