On an inverse problem of nonlinear imaging with fractional damping
On an inverse problem of nonlinear imaging with fractional damping
复制标题
DOI：
10.1090/mcom/3683
复制
发表时间：
2021-03
期刊：
影响因子：
--
通讯作者：
B. Kaltenbacher;W. Rundell
中科院分区：
文献类型：
--
作者：
B. Kaltenbacher;W. Rundell
本文考虑压力公式中的衰减的韦斯特丙酮方程。衰减是由文献中提出的各种模型，其特征在于包含非本地运营商，使幂律阻尼，而不是指数的经典模型。我们的目标是恢复方程中的空间相关系数的反问题，非线性参数$\kappa（x）$，在什么成为一个非线性双曲方程的非局部项。叠加的测量数据是在域的子集或其边界上取得的时间轨迹。我们将显示从$\kappa$到用于恢复它的叠加数据的线性化映射的注入性，并从这个基础上开发和分析牛顿型计划，以实现其有效恢复。
This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion of non-local operators that give power law damping as opposed to the exponential of classical models. The goal is the inverse problem of recovering a spatially dependent coefficient in the equation, the parameter of nonlinearity $\kappa(x)$, in what becomes a nonlinear hyperbolic equation with nonlocal terms. The overposed measured data is a time trace taken on a subset of the domain or its boundary. We shall show injectivity of the linearised map from $\kappa$ to the overposed data used to recover it and from this basis develop and analyse Newton-type schemes for its effective recovery.