Decay property of regularity-loss type and application to some nonlinear hyperbolic-elliptic system

Takafumi Hosono, Shuichi Kawashima

研究成果: Contribution to journalArticle査読

67 被引用数 (Scopus)

抄録

We discuss the global solvability and asymptotic behavior of solutions to the Cauchy problem for some nonlinear hyperbolic-elliptic system with a fourth-order elliptic part. This system is a modified version of the simplest radiating gas model and verifies a decay property of regularity-loss type. Such a dissipative structure also appears in the dissipative Timoshenko system studied by Rivera and Racke. This dissipative property is very weak in high frequency region and causes the difficulty in deriving the desired a priori estimates for global solutions to the nonlinear problem. In fact, it turns out that the usual energy method does not work well. We overcome this difficulty by employing a time-weighted energy method which is combined with the optimal decay for lower order derivatives of solutions, and we establish a global existence and asymptotic decay result. Furthermore, we show that the solution has an asymptotic self-similar profile described by the Burgers equation as time tends to infinity.

本文言語英語
ページ(範囲)1839-1859
ページ数21
ジャーナルMathematical Models and Methods in Applied Sciences
16
11
DOI
出版ステータス出版済み - 11 2006

All Science Journal Classification (ASJC) codes

  • モデリングとシミュレーション
  • 応用数学

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