Determining kernels in linear viscoelasticity

Abstract

In this work, we investigate the inverse problem of determining the kernel functions that best describe the mechanical behavior of a complex medium modeled by a general nonlocal viscoelastic wave equation. To this end, we minimize a tracking-type data misfit function under this PDE constraint. We perform the well-posedness analysis of the state and adjoint problems and, using these results, rigorously derive the first-order sensitivities. Numerical experiments in a three-dimensional setting illustrate the method.

References in corpus (7)

• The AAA algorithm for rational approximation
• A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
• Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation
• Optimal scalar products in the Standard Linear Viscoelastic Model
• Comparison of fractional wave equations for power law attenuation in ultrasound and elastography
• Fraction diffusion: Recovering the distributed fractional derivative from overposed data
• Well-posedness of the fractional Zener wave equation for heterogenous viscoelastic materials

Cited by in corpus (3)

• Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton type methods via range invariance
• On the optimal choice of the illumination function in photoacoustic tomography
• Inverse problem for wave equation of memory type with acoustic boundary conditions: Global solvability