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.
@article{arxiv.2112.14071,
title = {Determining kernels in linear viscoelasticity},
author = {Barbara Kaltenbacher and Ustim Khristenko and Vanja Nikolić and Mabel Lizzy Rajendran and Barbara Wohlmuth},
journal= {arXiv preprint arXiv:2112.14071},
year = {2022}
}