DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR SOME HYPERBOLIC-ELLIPTIC SYSTEM

• KUBO Takekiyo

  Graduate School of Mathematics Kyushu University

• KAWASHIMA Shuichi

  Faculty of Mathematics Kyushu University

抄録

We study the decay property of a certain nonlinear hyperbolic-elliptic system with 2mth-order elliptic part, which is a modified version of the simplest radiating gas model. It is proved that, for m ≥ 2, the system verifies a decay property of the regularity-loss type that is characterized by the parameter m. This dissipative property is very weak in the high-frequency region and causes a difficulty in showing the global existence of solutions to the nonlinear problem. By employing the time-weighted energy method together with the optimal decay for lower-order derivatives of solutions, we overcome this difficulty and establish a global existence and asymptotic decay result. Furthermore, we show that the solution approaches the nonlinear diffusion wave described by the self-similar solution of the Burgers equation as time tends to infinity.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 63 (1), 139-159, 2009

  九州大学大学院数理学研究院

キーワード

• hyperbolic-elliptic system
• decay property of regularity-loss type
• weighted energy method
• asymptotic behavior

詳細情報

• CRID: 1390282680204395776
• NII論文ID: 130000135276
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.63.139
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/63/1/63_1_139/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可