Remarks on the ill-posedness results for the drift diffusion system (Harmonic Analysis and Nonlinear Partial Differential Equations)

• イワブチ, ツカサ

  Osaka City University

• オガワ, タカヨシ

  Tohoku University

抄録

The ill-posedness issue is considered for the drift-diffusion system of bipolar type. It is shown that the continuous dependence on initial data does not hold generally in the scaling invariant Besov spaces. The scaling invariant Besov spaces are dot{B}{p, $sigma$}^{-2+frac{n}{p}(mathbb{R}^{n}) with 1 leq p, $sigma$leq 1, and the reason on the optimality of the case p=2n is explained to obtain the well-posedness and the ill-posedness for the drift diffusion system of bipolar type with the attention to the divergence form structure of the nonlinear term. The scaling invariant spaces for the heat equation with the nonlinear term u^{2} are same as those for the drift diffusion system and the difference is also indicated on the ill-posedness results between the heat equation and the drift diffusion system.

"Harmonic Analysis and Nonlinear Partial Differential Equations". June 30～July 2, 2014. edited by Hideo Kubo and Mitsuru Sugimoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

収録刊行物

• 数理解析研究所講究録別冊

  数理解析研究所講究録別冊 B56 31-41, 2016-04

  Research Institute for Mathematical Sciences, Kyoto University

キーワード

• 35K08
• 35K55
• Ill-posedness
• Besov spaces
• Drift diffusion equation

詳細情報

• CRID: 1050845763182222464
• NII論文ID: 110010059425
• NII書誌ID: AA12196120
• ISSN: 18816193
• HANDLE: 2433/241320
• 本文言語コード: en
• 資料種別: departmental bulletin paper
• データソース種別:
  • IRDB
  • CiNii Articles