论文标题
卡尔曼通过边界数据估计了耦合定量热声方程的一些反问题。第一部分：卡尔曼估计
Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates
论文作者
论文摘要
在本文中，我们考虑了耦合定量热声方程的Carleman估计和反问题。在第一部分中，我们通过假设系数满足适当的条件并采用通常的重量函数$φ（x，t）= {\ rm e}^{\ rm e}^{λψ（x，x，x，x，t）} $，从而建立了耦合定量热声方程的卡尔曼估计值$ψ（x，t）= \ left | x-x_ {0} \ right |^{2}-β\ left（t-t_0 \ right）^{2}+βT_0^{2} $ $ x $ for $ x $ for $ x $ in $ \ \ mathbb {r} t）$，其中$ t_0 = t/2 $。我们将讨论卡尔曼估计的应用在接下来的第二部分论文中的耦合定量热声方程的某些反问题上的应用。
In this paper, we consider Carleman estimates and inverse problems for the coupled quantitative thermoacoustic equations. In Part I, we establish Carleman estimates for the coupled quantitative thermoacoustic equations by assuming that the coefficients satisfy suitable conditions and taking the usual weight function $φ(x,t)={\rm e}^{λψ(x,t)}$, $ψ(x,t)=\left|x-x_{0}\right|^{2}-β\left(t-t_0\right)^{2}+βt_0^{2}$ for $x$ in a bounded domain in $\mathbb{R}^{n}$ with $C^{3}$-boundary and $t\in(0, T)$, where $t_0=T/2$. We will discuss applications of the Carleman estimates to some inverse problems for the coupled quantitative thermoacoustic equations in the succeeding Part II paper \cite{part II}.
