Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach
<|reference_start|>Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach: In this paper we consider the time dependent Porous Medium Equation, $u_t = \Delta u^\gamma$ with real polytropic exponent $\gamma>1$, subject to a homogeneous Dirichlet boundary condition. We are interested in recovering $\gamma$ 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 $\gamma$. An upper bound for the error between the exact and recovered $\gamma$ is then showed. Finally, numerical investigations are carried out in two dimensions.<|reference_end|>
@article{karakazian2024recovering,
    title={Recovering the Polytropic Exponent in the Porous Medium Equation:
  Asymptotic Approach},
    author={Hagop Karakazian, Toni Sayah, Faouzi Triki},
    journal={arXiv preprint arXiv:2402.19056},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.19056},
    primaryClass={math.NA cs.NA}
}