The pulsating orb: solving the wave equation outside a ball

被引：7

作者：

Martin, P. A. ^{[1
]}

机构：

[1] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2016年 / 472卷 / 2189期

关键词：

wave equation; acoustics; Laplace transform; transient problems; time domain; sound pulses; PARTIAL-DIFFERENTIAL-EQUATIONS; BOUNDARY VALUE-PROBLEMS; TIME BIE METHOD; TRANSIENT DIFFRACTION; EXTERIOR; PULSE;

D O I：

10.1098/rspa.2016.0037

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Transient acoustic waves are generated by the oscillations of an object or are scattered by the object. This leads to initial-boundary value problems (IBVPs) for the wave equation. Basic properties of this equation are reviewed, with emphasis on characteristics, wavefronts and compatibility conditions. IBVPs are formulated and their properties reviewed, with emphasis on weak solutions and the constraints imposed by the underlying continuum mechanics. The use of the Laplace transform to treat the IBVPs is also reviewed, with emphasis on situations where the solution is discontinuous across wavefronts. All these notions are made explicit by solving simple IBVPs for a sphere in some detail.

引用

页数：20