## 抄録

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space. We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection. In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t^{-α/4} as t → ∞, provided that the initial perturbation is in the weighted space L^{2}_{α}=L^{2}(ℝ_{+};(1+x)^{α}dx). This convergence rate t^{-α/4} is weaker than the one for the non-degenerate case and requires the restriction α < α_{*}(q), where α_{*}(q) is the critical value depending only on the degeneracy exponent q. Such a restriction is reasonable because the corresponding linearized operator for viscous conservation laws cannot be dissipative in L^{2}_{α} for α > α ^{*}(q) with another critical value α^{*}(q). Our stability analysis is based on the space-time weighted energy method in which the spatial weight is chosen as a function of the degenerate stationary wave.

本文言語 | English |
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ページ（範囲） | 735-762 |

ページ数 | 28 |

ジャーナル | Archive for Rational Mechanics and Analysis |

巻 | 198 |

号 | 3 |

DOI | |

出版ステータス | Published - 2010 9 17 |

外部発表 | はい |

## ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering