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arXiv · 2402.19056

Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach

Hagop Karakazian·Toni Sayah·Faouzi Triki
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Abstract

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.

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Hagop Karakazian, Toni Sayah, Faouzi Triki. 2024-02-29. Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach. https://arxiv.org/abs/2402.19056

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