论文标题
临界和亚临界半线性不均匀和各向异性弹性波方程的稳定
Stabilization of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation
论文作者
论文摘要
{\ bf Abstract} \，\，我们证明了临界和亚临界半联合性和各向异性弹性波方程的指数衰减，并在有界域上局部分布了阻尼。与以前的结果相比，一种新颖性是给出不均匀和各向异性培养基的可检查条件。另一个新颖性是建立一个框架来研究阻尼的半连续性和各向异性弹性波方程的稳定性，这很难应用Carleman估计来处理。我们开发了半弹性波方程的Morawetz估计值和紧凑型唯一性参数，以证明独特的延续，可观察性不平等和稳定结果。 它指出我们的证明与经典方法不同（参见Dehman等人\ cite {Zyy11}，Joly等人。
{\bf Abstract} \,\,We prove exponential decay of the critical and subcritical semilinear inhomogeneous and anisotropic elastic wave equation with locally distributed damping on bounded domain. One novelty compared to previous results, is to give a checkable condition of the inhomogeneous and anisotropic medias. Another novelty is to establish a framework to study the stability of the damped semilinear inhomogeneous and anisotropic elastic wave equation, which is hard to apply Carleman estimates to deal with. We develop the Morawetz estimates and the compactness-uniqueness arguments for the semiliear elastic wave equation to prove the unique continuation, observability inequality and stabilization result. It is pointing that our proof is different from the classical method (See Dehman et al.\cite{ZYY11}, Joly et al.\cite{ZYY16} and Zuazua \cite{ZYY43}), which succeeds for the subcritical semilinear wave equation and fails for the critical semilinear wave equation.
