Explicit decay rates for a generalized Boussinesq-Burgers system
Explicit decay rates for a generalized Boussinesq-Burgers system
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DOI：
10.1016/j.aml.2019.106054
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Neng Zhu;Zheng-rong Liu;F. Wang;Kun Zhao
中科院分区：
文献类型：
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作者：
Neng Zhu;Zheng-rong Liu;F. Wang;Kun Zhao
本文关注广义 Boussinesq-Burgers 系统柯西问题经典解的长期渐近行为： u t+(u w) x= ε u x x, x∈ R, t> 0, w t+ u γ+ w 2 2 x= μ w x x+ δ w x x t, x∈ R, t> 0,(u, w)(x, 0)=(u 0, w 0)(x), xε R，其中 γ≥ 2，ε、μ 和 δ 为正常数。通过利用时间加权能量方法，我们在初始数据的温和条件下确定了柯西问题经典解的显式衰减率。这概括了 Zhu 和 Liu（2016）通过将指数 γ 从单个值扩展到半实数线而获得的先前结果。
This paper is concerned with the long-time asymptotic behavior of classical solutions to the Cauchy problem for the generalized Boussinesq–Burgers system: u t+(u w) x= ε u x x, x∈ R, t> 0, w t+ u γ+ w 2 2 x= μ w x x+ δ w x x t, x∈ R, t> 0,(u, w)(x, 0)=(u 0, w 0)(x), x∈ R, where γ≥ 2, ε, μ and δ are positive constants. By utilizing time-weighted energy methods, we identify the explicit decay rates of classical solutions to the Cauchy problem under mild conditions on the initial data. This generalizes the previous result obtained in Zhu and Liu (2016) by extending the exponent γ from a single value to the half real line.