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

Yoshihiro Ueda, Shuichi Kawashima

研究成果: ジャーナルへの寄稿記事

7 引用 (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.

元の言語英語
ページ(範囲)147-179
ページ数33
ジャーナルJournal of Hyperbolic Differential Equations
4
発行部数1
出版物ステータス出版済み - 3 2007

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Semilinear Systems
Decay of Solutions
Damped Wave Equation
Pointwise Estimates
Large Time Behavior
Nonlinear Diffusion
Self-similar Solutions
Behavior of Solutions
Hyperbolic Systems
Burgers Equation
Fundamental Solution
Global Existence
Convection
Initial Value Problem
Infinity
Tend
Term

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Analysis

これを引用

Large time behavior of solutions to a semilinear hyperbolic system with relatxaion. / Ueda, Yoshihiro; Kawashima, Shuichi.

:: Journal of Hyperbolic Differential Equations, 巻 4, 番号 1, 03.2007, p. 147-179.

研究成果: ジャーナルへの寄稿記事

Ueda, Yoshihiro ; Kawashima, Shuichi. / Large time behavior of solutions to a semilinear hyperbolic system with relatxaion. :: Journal of Hyperbolic Differential Equations. 2007 ; 巻 4, 番号 1. pp. 147-179.
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