Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay

Danhua Wang; Gang Li; Biqing Zhu

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Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay

机译：具有粘弹性项和时滞的传递问题解的指数能量衰减

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In our previous work (Journal of Nonlinear Science and Applications 9: 1202–1215, 2016), we studied the well-posedness and general decay rate for a transmission problem in a bounded domain with a viscoelastic term and a delay term. In this paper, we continue to study the similar problem but without the frictional damping term. The main difficulty arises since we have no frictional damping term to control the delay term in the estimate of the energy decay. By introducing suitable energy and Lyapunov functionals, we establish an exponential decay result for the energy.

机译：在我们之前的工作中（非线性科学与应用学报9：1202-1215，2016），我们研究了带粘弹性项和延迟项的有界域中传输问题的适定性和一般衰减率。在本文中，我们将继续研究类似的问题，但没有摩擦阻尼项。由于我们没有摩擦阻尼项来控制能量衰减估计中的延迟项，因此出现了主要困难。通过引入合适的能量和李雅普诺夫泛函，我们建立了能量的指数衰减结果。

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《Mathematics》 |2016年第2期|共页
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Danhua Wang; Gang Li; Biqing Zhu;
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2. Global existence and energy decay of solutions to a viscoelastic Timoshenko beam system with a nonlinear delay term [J] . Djilali Laid, Benaissa Abbes, Benaissa Abdelkader Applicable Analysis . 2016,第10a12期

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5. Precise energy decay rates for some viscoelastic and thermo-viscoelastic rods. [D] . Inch, Scott Eugene. 1992

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7. Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay [O] . Danhua Wang, Gang Li, Biqing Zhu 2016

机译：具有粘弹性项和时滞的传输问题解的指数能量衰减

Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay

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