# American Institute of Mathematical Sciences

August  2019, 12(4): 923-944. doi: 10.3934/krm.2019035

## Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws

 1 Graduate School of Mathematics, Kyushu University, Fukuoka 819-0395, Japan 2 Department of Applied Mathematics, Kumamoto University, Kumamoto 860-8555, Japan 3 Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan

* Corresponding author: Kenta Nakamura

Received  November 2018 Published  May 2019

This paper is concerned with the rarefaction waves for a model system of hyperbolic balance laws in the whole space and in the half space. We prove the asymptotic stability of rarefaction waves under smallness assumptions on the initial perturbation and on the amplitude of the waves. The proof is based on the $L^2$ energy method.

Citation: Kenta Nakamura, Tohru Nakamura, Shuichi Kawashima. Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws. Kinetic & Related Models, 2019, 12 (4) : 923-944. doi: 10.3934/krm.2019035
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