Electron. J. Differential Equations, Vol. 2019 (2019), No. 131, pp. 1-14.

Acoustic scattering from open cavities in the time domain

Bo Chen, Fuming Ma, Yukun Guo

This article concerns acoustic scattering from two-dimensional open cavities in the time domain. A transparent boundary condition is provided to reformulate the problem as an equivalent initial boundary value problem in the interior region of the open cavity. The well-posedness, that is, the existence, uniqueness and stability of the solution to the reduced problem, is proved via a "Laplace domain" to time domain analysis. Moreover, time domain boundary integral equations for the reduced problem are established.

Submitted March 8, 2019. Published December 16, 2019.
Math Subject Classifications: 35L20, 35B35, 35A22.
Key Words: Time domain acoustic scattering; open cavity; transparent boundary condition; well-posedness; boundary integral equation.

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Bo Chen
College of Science
Civil Aviation University of China
Tianjin 300300, China
email: charliecb@163.com
  Fuming Ma
Institute of Mathematics
Jilin University
Changchun 130012, China
email: mfm@jlu.edu.cn
  Yukun Guo
School of Mathematics
Harbin Institute of Technology
Harbin 150001, China
email: ykguo@hit.edu.cn

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