Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Oleg Yu. Imanuvilov; Yavar Kian; Masahiro Yamamoto

Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Analysis of PDEs 2020-09-22 v1

Authors: Oleg Yu. Imanuvilov , Yavar Kian , Masahiro Yamamoto

Abstract

For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$ , we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also we prove similar results for the corresponding inverse source problem.

Keywords

inverse parabolic problem carleman estimate conditional stability lateral boundary data inverse source problem

Cite

@article{arxiv.2009.09710,
  title  = {Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate},
  author = {Oleg Yu. Imanuvilov and Yavar Kian and Masahiro Yamamoto},
  journal= {arXiv preprint arXiv:2009.09710},
  year   = {2020}
}

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