Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929283930259456 |
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| author | Karakazian, Hagop Sayah, Toni Triki, Faouzi |
| author_facet | Karakazian, Hagop Sayah, Toni Triki, Faouzi |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach Karakazian, Hagop Sayah, Toni Triki, Faouzi Numerical Analysis 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. |
| title | Recovering the Polytropic Exponent in the Porous Medium Equation: Asymptotic Approach |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.19056 |