On the porous-elastic system with Kelvin-Voigt damping

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• 作者：M.L. Santos ; ^{ls@ufpa.br" class="auth_mail" title="E-mail the corresponding author} ; D.S. Almeida Jú ; nior ^{dilberto@ufpa.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Porous elastic system ; Kelvin&ndash ; Voigt damping ; Analyticity ; Exponential decay
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：498-512
• 全文大小：362 K

文摘

In this article we are considering the one-dimensional equations of a homogeneous and isotropic porous elastic solid with Kelvin–Voigt damping. We prove that the semigroup associated with the system (1.3) with Dirichlet–Dirichlet boundary conditions or Dirichlet–Neumann boundary conditions is analytic and consequently exponentially stable. On the other hand, we prove that the system (1.3) with Dirichlet–Neumann boundary conditions has lack of exponential decay and it decays as $\frac{1}{\sqrt{t}}$ for the case ${\gamma }_1>0,{\gamma }_2=0$ or ${\gamma }_1=0,{\gamma }_2>0$. Moreover, we prove that this rate is optimal. We apply the main results for the Timoshenko model.