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日仏数学拠点FJ-LMIセミナー
過去の記録 ～05/02｜次回の予定｜今後の予定 05/03～
| 担当者 | 小林俊行, ミカエル ペブズナー |
|---|
2024年03月11日(月)
13:30-14:30 数理科学研究科棟(駒場) 117号室
Florian SALIN 氏 (Université de Lyon - Tohoku University)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
https://fj-lmi.cnrs.fr/seminars/
Florian SALIN 氏 (Université de Lyon - Tohoku University)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
[ 講演概要 ]
This talk will discuss a fractional nonlinear diffusion equation on bounded domains. This equation arises by combining fractional (in space) diffusion, with a nonlinearity of porous medium or fast diffusion type. It is known that, in the porous medium case, the energy of the solutions to this equation decays algebraically, and in the fast diffusion case, solutions extinct in finite time. Based on these estimates, we will study the fine large-time asymptotic behavior of the solutions. In particular, we will show that the solutions approach separate variable solutions as the time converges to infinity in the porous medium case, or as it converges to the extinction time in the fast diffusion case. However, the extinction time is not known analytically, and to compute it, we will introduce a numerical scheme that satisfies the same decay estimates as the continuous equation.
[ 講演参考URL ]This talk will discuss a fractional nonlinear diffusion equation on bounded domains. This equation arises by combining fractional (in space) diffusion, with a nonlinearity of porous medium or fast diffusion type. It is known that, in the porous medium case, the energy of the solutions to this equation decays algebraically, and in the fast diffusion case, solutions extinct in finite time. Based on these estimates, we will study the fine large-time asymptotic behavior of the solutions. In particular, we will show that the solutions approach separate variable solutions as the time converges to infinity in the porous medium case, or as it converges to the extinction time in the fast diffusion case. However, the extinction time is not known analytically, and to compute it, we will introduce a numerical scheme that satisfies the same decay estimates as the continuous equation.
https://fj-lmi.cnrs.fr/seminars/
