Determining damping terms in fractional wave equations

Abstract

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 on the relation between the asymptotics of solutions in time and Laplace domain. Also 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. Additionally, we provide an analysis of the forward problem, a multiterm fractional wave equation.

Cited by in corpus (4)

• Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
• Initial-boundary value problems for coupled systems of time-fractional diffusion equations
• Forward and backward problems for coupled subdiffusion systems
• Exponential stability for an infinite memory wave equation with frictional damping and logarithmic nonlinear terms