Determining damping terms in fractional wave equations
Determining damping terms in fractional wave equations
复制标题
DOI：
10.1088/1361-6420/ac6b31
复制
发表时间：
2021-11
期刊：
影响因子：
2.1
通讯作者：
B. Kaltenbacher;W. Rundell
中科院分区：
文献类型：
--
作者：
B. Kaltenbacher;W. Rundell
本文讨论了恢复波动方程中任意数量分数阶阻尼项的反问题。我们开发了几种方法的唯一性和重建，其中一些依赖于Tauberian定理，提供时间和拉普拉斯域的解决方案的渐近行为之间的关系。另外恢复空间相关系数或初始数据的可能性进行了讨论。由此产生的方法重建系数和分数阶在这些方面进行了测试。此外，我们提供了一个多项分数阶波动方程的正问题的分析。
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems that provide relations between the asymptotic behaviour of solutions in time and Laplace domains. The possibility of additionally recovering space-dependent coefficients or initial data is discussed. The resulting methods for reconstructing coefficients and fractional orders in these terms are tested numerically. In addition, we provide an analysis of the forward problem consisting of a multiterm fractional wave equation.