The Moore-Gibson-Thompson equation with memory in the critical case

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• 作者：Filippo Dell'Oro^a ; ^{filippo.delloro@polimi.it" class="auth_mail" title="E-mail the corresponding author} ; Irena Lasiecka^b ; ^c ; ^{lasiecka@memphis.edu" class="auth_mail" title="E-mail the corresponding author} ; Vittorino Pata^a ; ^{vittorino.pata@polimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B35 ; 35G05 ; 45D05 ; 47D06
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 October 2016
• 年：2016
• 卷：261
• 期：7
• 页码：4188-4222
• 全文大小：422 K

文摘

We consider the following abstract version of the Moore–Gibson–Thompson equation with memory depending on the parameters α,β,γ>0$\alpha ,\beta ,\gamma >0$, where A is strictly positive selfadjoint linear operator and g   is a convex (nonnegative) memory kernel. In the subcritical case αβ>γ$\alpha \beta >\gamma$, the related energy has been shown to decay exponentially in [19]. Here we discuss the critical case αβ=γ$\alpha \beta =\gamma$, and we prove that exponential stability occurs if and only if A is a bounded operator. Nonetheless, the energy decays to zero when A is unbounded as well.