POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS

doi:10.1007/s10473-020-0409-x

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 1001-1019.doi: 10.1007/s10473-020-0409-x

POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS

李念英

College of Science, Binzhou University, Binzhou 256600, China

收稿日期:2019-04-25 修回日期:2019-08-15 出版日期:2020-08-25 发布日期:2020-08-21
作者简介:Nianying LI,E-mail:lnying81@163.com
基金资助:
Supported by Binzhou University (BZXYL1402).

POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS

Nianying LI

College of Science, Binzhou University, Binzhou 256600, China

Received:2019-04-25 Revised:2019-08-15 Online:2020-08-25 Published:2020-08-21
Supported by:
Supported by Binzhou University (BZXYL1402).

摘要/Abstract

摘要： In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions (n≥4). We use the Green's function method. Our approach is on the basis of the detailed analysis of the Green's function of the linearized system. We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions. It is shown that the solution exhibits a generalized Huygens principle.

关键词: viscous wave equation, pointwise estimate, even dimensions

Abstract: In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions (n≥4). We use the Green's function method. Our approach is on the basis of the detailed analysis of the Green's function of the linearized system. We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions. It is shown that the solution exhibits a generalized Huygens principle.

Key words: viscous wave equation, pointwise estimate, even dimensions

中图分类号:

35M20

李念英. POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS[J]. 数学物理学报(英文版), 2020, 40(4): 1001-1019.

Nianying LI. POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS[J]. Acta mathematica scientia,Series B, 2020, 40(4): 1001-1019.

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POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS

POINTWISE ESTIMATES OF SOLUTIONS FOR THE NONLINEAR VISCOUS WAVE EQUATION IN EVEN DIMENSIONS

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