English

Determination of source and initial values for acoustic equations with a time-fractional attenuation

Analysis of PDEs 2021-11-10 v1

Abstract

We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or photoacoustic tomography. We prove a stability estimate for each of these two problems, with the aid of a Carleman estimate specifically designed for the governing equation.

Keywords

Cite

@article{arxiv.2111.05240,
  title  = {Determination of source and initial values for acoustic equations with a time-fractional attenuation},
  author = {Xinchi Huang and Yavar Kian and Eric Soccorsi and Masahiro Yamamoto},
  journal= {arXiv preprint arXiv:2111.05240},
  year   = {2021}
}