论文标题
具有非平滑系数的本地耦合波的弹性/粘弹性传输问题的稳定性结果
Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients
论文作者
论文摘要
我们研究了只有一种内部粘弹性阻尼的局部耦合波方程的稳定。本文的主要新颖性是阻尼和耦合系数都不平滑。首先，使用Arendt-Batty的一般标准，结合了独特的结果，我们证明了我们的系统非常稳定。接下来，使用频谱方法，我们证明了系统的非指数（均匀）稳定性。最后，使用频域方法，结合分段乘数技术和满足某些普通微分方程的新乘数的构建，我们表明系统的平滑溶液的能量在T^{ - 1}的多个百膜中衰减。
We investigate the stabilization of a locally coupled wave equations with only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty in this paper is that both the damping and the coupling coefficients are non smooth. First, using a general criteria of Arendt-Batty, combined with an uniqueness result, we prove that our system is strongly stable. Next, using a spectrum approach, we prove the non-exponential (uniform) stability of the system. Finally, using a frequency domain approach, combined with a piecewise multiplier technique and the construction of a new multiplier satisfying some ordinary differential equations, we show that the energy of smooth solutions of the system decays polynomially of type t^{-1}.
