Decay estimates for hyperbolic balance laws

Shuichi Kawashima, Wen An Yong

Research output: Contribution to journalArticle

26 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalZeitschrift fur Analysis und ihre Anwendung
Volume28
Issue number1
DOIs
Publication statusPublished - Jan 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

Cite this

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

In: Zeitschrift fur Analysis und ihre Anwendung, Vol. 28, No. 1, 01.01.2009, p. 1-33.

Research output: Contribution to journalArticle

Kawashima, Shuichi ; Yong, Wen An. / Decay estimates for hyperbolic balance laws. In: Zeitschrift fur Analysis und ihre Anwendung. 2009 ; Vol. 28, No. 1. pp. 1-33.
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