论文标题
半线性波方程的逆问题：数值研究
An inverse problem for a semi-linear wave equation: a numerical study
论文作者
论文摘要
我们考虑一个逆问题，即恢复与半线性波方程相关的潜力，其二次非线性为$ 1 + 1 $尺寸。我们开发了一个数值方案，以确定横向边界上嘈杂的Dirichlet到Neumann地图的电势。该方案基于最近的高阶线性化方法[20]。我们还提出了一种通过Tikhonov正则化来估计嘈杂数据的二维导数的方法。使用Dirichlet到Neumann地图的合成嘈杂测量值对方法进行了测试。给出了潜在功能重建的各种示例。
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy Dirichlet-to-Neumann map on the lateral boundary. The scheme is based on the recent higher order linearization method [20]. We also present an approach to numerically estimating two-dimensional derivatives of noisy data via Tikhonov regularization. The methods are tested using synthetic noisy measurements of the Dirichlet-to-Neumann map. Various examples of reconstructions of the potential functions are given.
