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Bibliographic Details
Main Authors: Karakazian, Hagop, Sayah, Toni, Triki, Faouzi
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.19056
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Table of Contents:
  • In this paper we consider the time dependent Porous Medium Equation, $u_t = Δu^γ$ with real polytropic exponent $γ>1$, subject to a homogeneous Dirichlet boundary condition. We are interested in recovering $γ$ from the knowledge of the solution $u$ at a given large time $T$. Based on an asymptotic inequality satisfied by the solution $u(T)$, we propose a numerical algorithm allowing us to recover $γ$. An upper bound for the error between the exact and recovered $γ$ is then showed. Finally, numerical investigations are carried out in two dimensions.