DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR SOME HYPERBOLIC-ELLIPTIC SYSTEM
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- KUBO Takekiyo
- Graduate School of Mathematics Kyushu University
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- KAWASHIMA Shuichi
- Faculty of Mathematics Kyushu University
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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
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- 九州数学雑誌
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九州数学雑誌 63 (1), 139-159, 2009
九州大学大学院数理学研究院
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詳細情報 詳細情報について
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- CRID
- 1390282680204395776
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- NII論文ID
- 130000135276
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- NII書誌ID
- AA10994346
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- ISSN
- 18832032
- 13406116
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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- 使用不可