多维的一般的BBM-Burgers方程解的逐点估计

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 473-486.

• 论文 • 下一篇

多维的一般的BBM-Burgers方程解的逐点估计

张丹丹

上海交通大学数学系上海 200240

收稿日期:2013-05-27 修回日期:2013-12-20 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11071162, 11231006, 11171212, 11171213)资助

Pointwise Estimates for the Solution to the Multi-Dimensional Generalized BBM-Burgers Equation

ZHANG Dan-Dan

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Received:2013-05-27 Revised:2013-12-20 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11071162, 11231006, 11171212, 11171213)资助

摘要/Abstract

摘要：

研究Rⁿ中一般的BBM-Burgers方程解的渐进行为. 运用 Green 函数法和 Fourier 分析方法得到了在非零常状态u *附近小扰动解的逐点估计, 作为一个推论, 又得到了L^p(Rⁿ)(1≤p\≤∞)空间解的最佳的衰减估计.

关键词: BBM-Burgers方程, Green , 函数, 最佳衰减估计, 能量方法, 逐点估计

Abstract:

In this paper, the author focuses on the time-asymptotic behavior of solution for the scalar multi-dimensional generalized BBM-Burgers equation in the whole-space Rⁿ. By using Green's function method combined with Fourier analysis method, the author yields the pointwise estimates of the solution when the initial data is a small perturbation around the constant state u*, (u*≠0). As a corollary, the optimal decay rate in L^p(Rⁿ)(1≤p≤∞) space is obtained.

Key words: BBM-Burgers equation, Green´s function, Optimal decay estimates, Energy method, Pointwise estimates

中图分类号:

35B40

张丹丹. 多维的一般的BBM-Burgers方程解的逐点估计[J]. 数学物理学报, 2014, 34(3): 473-486.

ZHANG Dan-Dan. Pointwise Estimates for the Solution to the Multi-Dimensional Generalized BBM-Burgers Equation[J]. Acta mathematica scientia,Series A, 2014, 34(3): 473-486.

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多维的一般的BBM-Burgers方程解的逐点估计

Pointwise Estimates for the Solution to the Multi-Dimensional Generalized BBM-Burgers Equation

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