## Abstract

In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term є∂tu - ∇ ∙ (γ∇u^{m}) + λu^{q} = 0 with m > 1, m ^{-1} < q < √m, with the space dimension 2 or higher. This is a degenerate parabolic type quasilinear PDE which has been used as a model for phenomena in fields such as gas flow (through a porous medium), plasma physics, and population dynamics. In the case when γ = 1 a priori, we prove unique identifiability with data supported in an arbitrarily small part of the boundary. Even for the global problem we improve on previous work by obtaining uniqueness with a finite (rather than infinite) time of observation and also by introducing the additional absorption term λu^{q}.

Original language | English |
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Pages (from-to) | 162-185 |

Number of pages | 24 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2023 |

## Keywords

- inverse problems
- nonlinear parabolic equations
- porous medium equation