Decay Estimates for Hyperbolic Balance Laws

  • Shuichi Kawashima

    Kyushu University, Fukuoka, Japan
  • Wen-An Yong

    Tsinghua University, Beijing, China


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 L2L^2-norm up to order s1s-1, provided that the initial data are in HsH^s. A key ingredient in our analysis is a time-weighted energy estimate, leading to a decay estimate for multi-dimensional problems without assuming the L1L^1 property on initial data.

Cite this article

Shuichi Kawashima, Wen-An Yong, Decay Estimates for Hyperbolic Balance Laws. Z. Anal. Anwend. 28 (2009), no. 1, pp. 1–33

DOI 10.4171/ZAA/1369