| Abstract: |
| In this talk we will introduce a general attenuated wave equation in the frequency domain using pseudo differential operator, which can be transformed into fractionally damped wave equations in the time domain. We will first explore how this general model relates to various fractionally damped wave equations and illustrate the connection among the initial conditions derived from physical principle. Next, we will establish the uniqueness of both direct and inverse problems associated with this framework. Additionally, we will discuss the ill-posedness of the inverse problem by analyzing the asymptotic behavior of the singular values of the forward operator. |
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