Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems in low dimensions

Jiang Xu*, Shuichi Kawashima

*この研究の対応する著者

研究成果: Article査読

8 被引用数 (Scopus)

抄録

Recently, a time-decay framework L2(Rn)∩B ˙2,∞-s(Rn)(s>0) has been given by [49] for linearized dissipative hyperbolic systems, which allows to pay less attention to the traditional spectral analysis. However, owing to interpolation techniques, those decay results for nonlinear hyperbolic systems hold true only in higher dimensions (n≥ 3), and the analysis in low dimensions (say, n= 1, 2) was left open. We try to give a satisfactory answer in the current work. First of all, we develop new time-decay properties on the frequency-localization Duhamel principle, and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n= 1, 2, by using a new technique which is the so-called "piecewise Duhamel principle" in localized time-weighted energy approaches compared to [49]. Finally, as direct applications, explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure, for instance, damped compressible Euler equations, the thermoelasticity with second sound, and Timoshenko systems with equal wave speeds.

本文言語English
ページ(範囲)2670-2701
ページ数32
ジャーナルJournal of Differential Equations
261
5
DOI
出版ステータスPublished - 2016 9 5
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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