## Abstract

There are several hybrid inverse problems for equations of the form ∇ · D(x) ∇ u - σ (x) u = 0in which we want to obtain the coefficients D and σ on a domain Ω when the solutions u are known. One approach is to use two solutions u_{1} and u_{2} to obtain a transport equation for the coefficient D, and then solve this equation inward from the boundary along the integral curves of a vector field X defined by u_{1} and u_{2}. Bal and Ren have shown that for any nontrivial choices of u_{1} and u_{2}, this method suffices to recover the coefficients almost everywhere on a dense set in Ω Bal and Ren in (Inv Prob 075003 [3]). This article presents an alternate proof of the same result from a dynamical systems point of view.

Original language | English |
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Title of host publication | Mathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019 |

Editors | Larisa Beilina, Maïtine Bergounioux, Michel Cristofol, Anabela Da Silva, Amelie Litman |

Pages | 15-20 |

Number of pages | 6 |

DOIs | |

State | Published - 2020 |

Event | Conference on Mathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019 - Marseille, France Duration: Apr 1 2019 → Apr 5 2019 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 328 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | Conference on Mathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019 |
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Country/Territory | France |

City | Marseille |

Period | 4/1/19 → 4/5/19 |

### Bibliographical note

Publisher Copyright:© Springer Nature Switzerland AG 2020.

## Keywords

- Hybrid inverse problems
- Reconstruction of coefficients
- Transport equation

## ASJC Scopus subject areas

- General Mathematics