## Abstract

We consider Holmgren-John's uniqueness theorem for a partial differential equation with a memory term when the coefficients of the equation are analytic. This is a special case of the general unique continuation property (UCP) for the equation if its coefficients are analytic. As in the case in the absence of a memory term, the Cauchy-Kowalevski theorem is the key to prove this. The UCP is an important tool in the analysis of related inverse problems. A typical partial differential equation with memory term is the equation describing viscoelastic behavior. Here, we prove the UCP for the viscoelastic equation when the relaxation tensor is analytic and allowed to be fully anisotropic.

Original language | English |
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Title of host publication | Time-dependent Problems in Imaging and Parameter Identification |

Publisher | Springer International Publishing |

Pages | 287-301 |

Number of pages | 15 |

ISBN (Electronic) | 9783030577841 |

ISBN (Print) | 9783030577834 |

DOIs | |

Publication status | Published - 2021 Feb 23 |

## All Science Journal Classification (ASJC) codes

- General Computer Science
- General Mathematics