### 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 W^{1,p} (1 ≤ p ≤ ∞) under smallness condition on the initial data. Moreover, we show that the solution approaches in W^{1,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 |

巻 | 4 |

発行部数 | 1 |

出版物ステータス | 出版済み - 3 2007 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Analysis

### これを引用

*Journal of Hyperbolic Differential Equations*,

*4*(1), 147-179.

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

研究成果: ジャーナルへの寄稿 › 記事

*Journal of Hyperbolic Differential Equations*, 巻. 4, 番号 1, pp. 147-179.

}

TY - JOUR

T1 - Large time behavior of solutions to a semilinear hyperbolic system with relatxaion

AU - Ueda, Yoshihiro

AU - Kawashima, Shuichi

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34447262298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34447262298&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34447262298

VL - 4

SP - 147

EP - 179

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

SN - 0219-8916

IS - 1

ER -