The lack of polynomial stability to mixtures with frictional dissipation

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• 作者：Francis F. Có ; rdova Puma^a ; ^{francis.cordova@ufsc.br" class="auth_mail" title="E-mail the corresponding author} ; Jaime E. Muñ ; oz Rivera^b ; ^{rivera@im.ufrj.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Strong stability ; Exponential stability ; Semigroups ; Mixture of materials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1882-1897
• 全文大小：359 K

文摘

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