Text only print
Full screen print
FJ-LMI Seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Organizer(s) | Toshiyuki Kobayashi, Michael Pevzner |
|---|
2024/03/11
13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Florian SALIN (Université de Lyon - 東北大学)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
https://fj-lmi.cnrs.fr/seminars/
Florian SALIN (Université de Lyon - 東北大学)
Fractional Nonlinear Diffusion Equation: Numerical Analysis and Large-time Behavior. (英語)
[ Abstract ]
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.
[ Reference 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/
