[2402.19056] Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach
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Mathematics > Numerical Analysis

arXiv:2402.19056 (math)
[Submitted on 29 Feb 2024 (v1), last revised 21 Mar 2024 (this version, v2)]

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

Authors: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2402.19056 [math.NA]
  (or arXiv:2402.19056v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2402.19056

Submission history

From: Toni Sayah [view email]
[v1] Thu, 29 Feb 2024 11:33:11 UTC (64 KB)
[v2] Thu, 21 Mar 2024 07:44:35 UTC (64 KB)
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