论文标题
从有限的边界测量集中恢复二阶双曲方程中的所有系数
Recover all Coefficients in Second-Order Hyperbolic Equations from Finite Sets of Boundary Measurements
论文作者
论文摘要
我们考虑恢复所有空间依赖系数的逆双曲线问题，这些系数是波速，阻尼系数，潜在系数和梯度系数，在二阶双曲方程中定义在具有足够平稳边界的开放式界面上。我们表明，通过适当地选择初始条件的有限对，我们可以唯一的，Lipschitz从其溶液的相应边界测量中稳定地恢复了所有这些系数。这些证明是基于尖锐的卡尔曼估计值，一般二阶双曲方程的连续可观察性不平等和规律性理论。
We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on an open bounded domain with smooth enough boundary. We show that by appropriately selecting finite pairs of initial conditions we can uniquely and Lipschitz stably recover all those coefficients from the corresponding boundary measurements of their solutions. The proofs are based on sharp Carleman estimate, continuous observability inequality and regularity theory for general second-order hyperbolic equations.
