论文标题
在$ w^{1，\ infty} $中的衰减中，对于有限域上的1D半连接式波动方程
On the decay in $W^{1,\infty}$ for the 1D semilinear damped wave equation on a bounded domain
论文作者
论文摘要
在本文中，我们研究了一个半线性波方程，在一个空间维度中具有非线性，时间依赖性阻尼。对于此问题，我们证明了时空域$（0,1）\ times [0，+\ infty）$在$ w^{1，\ infty} $中的适当性结果。然后，我们解决了零解决方案的时间 - 杂质稳定性的问题，并表明在适当的条件下，解决方案在空间$ w^{1，\ infty} $中以指数率的速率衰减为零。证明基于对一阶导数的相应半线性系统的分析，为此我们显示了不变域的承包属性。
In this paper we study a semilinear wave equation with nonlinear, time-dependent damping in one space dimension. For this problem, we prove a well-posedness result in $W^{1,\infty}$ in the space-time domain $(0,1)\times [0,+\infty)$. Then we address the problem of the time-asymptotic stability of the zero solution and show that, under appropriate conditions, the solution decays to zero at an exponential rate in the space $W^{1,\infty}$. The proofs are based on the analysis of the corresponding semilinear system for the first order derivatives, for which we show a contractive property of the invariant domain.
