Hardy type inequality and application to the stability of degenerate stationary waves

Shuichi Kawashima, Kazuhiro Kurata

研究成果: Contribution to journalArticle査読

8 被引用数 (Scopus)

抄録

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous conservation laws in the half space. It is proved 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 Lα2 = L2 (R+ ; (1 + x)α) for α < αc (q) : = 3 + 2 / q, where q is the degeneracy exponent. This restriction on α is best possible in the sense that the corresponding linearized operator cannot be dissipative in Lα2 for α > αc (q). Our stability analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant.

本文言語英語
ページ(範囲)1-19
ページ数19
ジャーナルJournal of Functional Analysis
257
1
DOI
出版ステータス出版済み - 7 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis

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