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Mathematics > Analysis of PDEs

arXiv:1811.12480 (math)
[Submitted on 29 Nov 2018]

Title:Analysis of transient acoustic scattering by an elastic obstacle

Authors:Peijun Li, Lei Zhang
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Abstract:Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional acoustic-elastic wave propagation problem in the time-domain. A compressed coordinate transformation is proposed to reduce equivalently the scattering problem into an initial-boundary value problem in a bounded domain over a finite time interval. The reduced problem is shown to have a unique weak solution by using the Galerkin method. The stability estimate and an a priori estimate with explicit time dependence are obtained for the weak solution. The reduced model problem is suitable for numerical simulations. The proposed method is applicable to many other time-domain scattering problems imposed in open domains.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1811.12480 [math.AP]
  (or arXiv:1811.12480v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1811.12480

Submission history

From: Peijun Li [view email]
[v1] Thu, 29 Nov 2018 20:53:18 UTC (152 KB)
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