| 日時： |
2007年10月25日（木） 14:00〜 |
| 場所： |
京都大学 工学研究科 11号館 2階 会議室 |
| 講演者： |
Prof. Naoufel Ben Abdallah (Institute of Mathematics of Toulouse, MIP University Paul Sabatier, Toulouse, France |
| 講演題目： |
A nonlinear conservation law derived from a kinetic equations: Entropy solutions and convergence after shock formation |
| 講演要旨： |
The high field limit for the semiconductor Boltzmann equation with Pauli exclusion terms is investigated. The limit problem is shown to have a unique solution for every given density. The particle density is finally proven to converge in the high field limit towards the solution of a nonlinear hyperbolic equation. By employing a new entropy, whose dissipation measures the departure from the high field equilibrium, convergence towards the unique entropic solution of the limiting conservation law is proven. The entropy is also used to construct kinetic shock profiles for entropic shocks and to prove non-existence of non-entropic shock profiles. Partial diffusion scaling will also be presented during the talk. |
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