Decay estimates for hyperbolic balance laws

Shuichi Kawashima, Wen An Yong

研究成果: ジャーナルへの寄稿記事

26 引用 (Scopus)

抄録

This work is concerned with time-decay properties of small-amplitude global smooth solutions to the initial value problem for hyperbolic systems of balance laws admitting an entropy and satisfying the stability condition. By using energy methods in both the physical space and the Fourier space, we obtain the optimal decay estimates of solutions and their derivatives in the L 2-norm up to order s - 1, provided that the initial data are in Hs. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1property on initial data.

元の言語英語
ページ(範囲)1-33
ページ数33
ジャーナルZeitschrift fur Analysis und ihre Anwendung
28
発行部数1
DOI
出版物ステータス出版済み - 1 1 2009

Fingerprint

Balance Laws
Decay Estimates
Initial value problems
Entropy
Derivatives
Global Smooth Solution
Weighted Estimates
Energy Estimates
Energy Method
Hyperbolic Systems
Stability Condition
Initial Value Problem
Decay
Norm
Derivative

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

これを引用

Decay estimates for hyperbolic balance laws. / Kawashima, Shuichi; Yong, Wen An.

:: Zeitschrift fur Analysis und ihre Anwendung, 巻 28, 番号 1, 01.01.2009, p. 1-33.

研究成果: ジャーナルへの寄稿記事

Kawashima, Shuichi ; Yong, Wen An. / Decay estimates for hyperbolic balance laws. :: Zeitschrift fur Analysis und ihre Anwendung. 2009 ; 巻 28, 番号 1. pp. 1-33.
@article{201ba10e792b48ce8659555ca1b2edff,
title = "Decay estimates for hyperbolic balance laws",
abstract = "This work is concerned with time-decay properties of small-amplitude global smooth solutions to the initial value problem for hyperbolic systems of balance laws admitting an entropy and satisfying the stability condition. By using energy methods in both the physical space and the Fourier space, we obtain the optimal decay estimates of solutions and their derivatives in the L 2-norm up to order s - 1, provided that the initial data are in Hs. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1property on initial data.",
author = "Shuichi Kawashima and Yong, {Wen An}",
year = "2009",
month = "1",
day = "1",
doi = "10.4171/ZAA/1369",
language = "English",
volume = "28",
pages = "1--33",
journal = "Zeitschrift fur Analysis und ihre Anwendung",
issn = "0232-2064",
publisher = "Heldermann Verlag",
number = "1",

}

TY - JOUR

T1 - Decay estimates for hyperbolic balance laws

AU - Kawashima, Shuichi

AU - Yong, Wen An

PY - 2009/1/1

Y1 - 2009/1/1

N2 - This work is concerned with time-decay properties of small-amplitude global smooth solutions to the initial value problem for hyperbolic systems of balance laws admitting an entropy and satisfying the stability condition. By using energy methods in both the physical space and the Fourier space, we obtain the optimal decay estimates of solutions and their derivatives in the L 2-norm up to order s - 1, provided that the initial data are in Hs. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1property on initial data.

AB - This work is concerned with time-decay properties of small-amplitude global smooth solutions to the initial value problem for hyperbolic systems of balance laws admitting an entropy and satisfying the stability condition. By using energy methods in both the physical space and the Fourier space, we obtain the optimal decay estimates of solutions and their derivatives in the L 2-norm up to order s - 1, provided that the initial data are in Hs. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1property on initial data.

UR - http://www.scopus.com/inward/record.url?scp=59649090714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59649090714&partnerID=8YFLogxK

U2 - 10.4171/ZAA/1369

DO - 10.4171/ZAA/1369

M3 - Article

AN - SCOPUS:59649090714

VL - 28

SP - 1

EP - 33

JO - Zeitschrift fur Analysis und ihre Anwendung

JF - Zeitschrift fur Analysis und ihre Anwendung

SN - 0232-2064

IS - 1

ER -