A distributional version of Kirchhoff's formula

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:359

Article

Laliena, Antonio R.¹  Sayas, Francisco-Javier² 

[1] Univ Zaragoza, EUPLA, Dep Matemat, La Almunia 50100, Spain

[2] Univ Zaragoza, Dep Matemat Aplicada, Ctr Politecn Super, Zaragoza 50018, Spain

关键词: Kirchhoff's formula;    Vector-valued distributions;    Convolution;   

DOI  :  10.1016/j.jmaa.2009.05.021

来源: Elsevier

【 摘 要 】

Kirchhoff's formula is the equivalent to Green's Third Theorem for transient waves, representing the solution of the three-dimensional wave equation in terms of its boundary data. In this classical result two retarded layer potentials appear. We show in this paper a precise description of these potentials as time convolution with adequate tempered distributions with values on operator spaces. With these potentials in hands we give a self-contained proof of the formula with minimal smoothness requirements. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free