Large time behavior of solutions to a semilinear hyperbolic system with relatxaion

Yoshihiro Ueda*, Shuichi Kawashima

*この研究の対応する著者

研究成果: Article査読

12 被引用数 (Scopus)

抄録

We are concerned with the initial value problem for a damped wave equation with a nonlinear convection term which is derived from a semilinear hyperbolic system with relaxation. We show the global existence and asymptotic decay of solutions in W1,p (1 ≤ p ≤ ∞) under smallness condition on the initial data. Moreover, we show that the solution approaches in W1,p (1 ≤ p ≤ ∞) the nonlinear diffusion wave expressed in terms of the self-similar solution of the Burgers equation as time tends to infinity. Our results are based on the detailed pointwise estimates for the fundamental solutions to the linearlized equation.

本文言語English
ページ(範囲)147-179
ページ数33
ジャーナルJournal of Hyperbolic Differential Equations
4
1
出版ステータスPublished - 2007 3月 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 数学 (全般)

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