Decay estimates for hyperbolic balance laws

Shuichi Kawashima*, Wen An Yong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2009
Externally publishedYes


  • Decay estimates
  • Entropy
  • Global smooth solutions
  • Hyperbolic balance laws
  • Stability condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Decay estimates for hyperbolic balance laws'. Together they form a unique fingerprint.

Cite this