Global solutions to the equation of viscoelasticity with fading memory

Shuichi Kawashima*

*この研究の対応する著者

研究成果: Article査読

19 被引用数 (Scopus)

抄録

The initial-history value problem for the one-dimensional equation of viscoelasticity with fading memory is studied in a situation that allows the kernel function to have integrable singularities in the first order derivative. It is proved that if the data are smooth and small, then a unique solution exists globally in time and converges to the equilibrium as time goes to infinity, provided that the kernel is strongly positive definite. This is an improvement on the previous result by W. J. Hrusa and J. A. Nohel (J. Differential Equations59, 1985, 388-412). Our proof is based on an energy method which makes use of properties of strongly positive definite kernels.

本文言語English
ページ(範囲)388-420
ページ数33
ジャーナルJournal of Differential Equations
101
2
DOI
出版ステータスPublished - 1993 2月
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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