带粘性的波动方程组解的逐点估计

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1421-1442.

带粘性的波动方程组解的逐点估计

吴志刚*(),缪小芳

东华大学理学院上海 201620

收稿日期:2018-05-14 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 吴志刚 E-mail:zgwu@dhu.edu.cn
基金资助:
上海市自然科学基金(16ZR1402100);中央高校基本科研业务费专项资金(2232019D3-43)

Pointwise Estimates for Systems of Wave Equations with Viscosity

Zhigang Wu*(),Xiaofang Miao

College of Science, Donghua University, Shanghai 201620

Received:2018-05-14 Online:2019-12-26 Published:2019-12-28
Contact: Zhigang Wu E-mail:zgwu@dhu.edu.cn
Supported by:
the NSF of Shanghai(16ZR1402100);the Fundamental Research Funds for the Central Universities(2232019D3-43)

摘要/Abstract

摘要：

论文研究了三维空间中带粘性项波动方程组解的逐点估计.同时考虑了两种非线性项：具有散度形式的非线性项和具有拉普拉斯形式的非线性项.利用长波和短波分解法，结合能量法和格林函数，得到大时间渐近形态解的逐点估计，并证实解的逐点估计可被相应具有不同传播速度（c₁≠ c₂）的广义惠更斯波控制.同时，还得到了p ≥ 1时最优的L^p衰减率.

关键词: 格林函数, 波动方程组, 一般惠更斯波

Abstract:

The Cauchy problem for two systems of wave equations with viscosity in dimension three is considered. By using the long wave and short wave decomposition method together with energy method and Green function, the pointwise estimates of the time-asymptotic shape of the solution are given, which exhibit two kinds of generalized Huygens' waves. As a byproduct, the optimal L^p-decay rates with p ≥ 1 of the solutions of these systems are also established.

Key words: Green function, Systems of wave equations with viscosity, Huygens' principle

中图分类号:

O175.2

吴志刚,缪小芳. 带粘性的波动方程组解的逐点估计[J]. 数学物理学报, 2019, 39(6): 1421-1442.

Zhigang Wu,Xiaofang Miao. Pointwise Estimates for Systems of Wave Equations with Viscosity[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1421-1442.

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