Recovery of Time-Dependent Damping Coefficients and Potentials Appearing in Wave Equations from Partial Data
Recovery of Time-Dependent Damping Coefficients and Potentials Appearing in Wave Equations from Partial Data
复制标题
从部分数据恢复波动方程中的瞬态阻尼系数和势能
DOI：
--
复制
发表时间：
2016
影响因子：
2
通讯作者：
Yavar Kian
中科院分区：
文献类型：
--
作者：
Yavar Kian
在$q =(0, t) imesomega $的波动方程$partial_t^2u-Delta_x u+a(t,x)partial_tu+q(t,x)u=0$中，利用$mathbb R^n$, $ngeq2$的有界域$ t > $和$Omega$ a$ mathcal C^2$，从$偏q$上解的部分观测值考虑确定时变阻尼系数$a$和时变势$q$的逆问题。更准确地说，我们寻找局部Q$的观测值，这些观测值允许在不涉及一组重要数据的情况下，唯一地确定一大类随时间变化的阻尼系数$a$和随时间变化的势$ Q$。从$偏Q$上的偏观测值证明了$ain W^{1,p}(Q)$, $p>n+1$和$qin L^ inty (Q)$的全局唯一确定。
We consider the inverse problem of determining a time-dependent damping coefficient $a$ and a time-dependent potential $q$, appearing in the wave equation $partial_t^2u-Delta_x u+a(t,x)partial_tu+q(t,x)u=0$ in $Q=(0,T) imesOmega$, with $T>0$ and $Omega$ a $ mathcal C^2$ bounded domain of $mathbb R^n$, $ngeq2$, from partial observations of the solutions on $partial Q$. More precisely, we look for observations on $partial Q$ that allow to determine uniquely a large class of time-dependent damping coefficients $a$ and time-dependent potentials $q$ without involving an important set of data. We prove global unique determination of $ain W^{1,p}(Q)$, with $p>n+1$, and $qin L^infty(Q)$ from partial observations on $partial Q$.