论文标题
在动态边界条件的波方程中识别源项
Identification of source terms in wave equation with dynamic boundary conditions
论文作者
论文摘要
本文研究了具有动态边界条件的波方程的反双曲线问题。它包括确定最终过度确定的强迫术语。首先，研究了Tikhonov函数的Fréchet可不同性，并通过相关的伴随问题解决方案获得梯度公式。然后，证明了梯度的Lipschitz连续性。此外，讨论了最小化问题的存在和唯一性。最后，通过结合梯度算法实施了一些用于重建内波力的数值实验。
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm.
