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Volume 30, Issue 1
Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

Tian Luan & Fuming Ma

Commun. Math. Res., 30 (2014), pp. 71-80.

Published online: 2021-05

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  • Abstract

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

  • Keywords

Helmholtz equation, rough surface, scattering problem.

  • AMS Subject Headings

47J30, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-71, author = {Luan , Tian and Ma , Fuming}, title = {Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {1}, pages = {71--80}, abstract = {

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/18989.html} }
TY - JOUR T1 - Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces AU - Luan , Tian AU - Ma , Fuming JO - Communications in Mathematical Research VL - 1 SP - 71 EP - 80 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/18989.html KW - Helmholtz equation, rough surface, scattering problem. AB -

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

Tian Luan & Fuming Ma. (2021). Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces. Communications in Mathematical Research . 30 (1). 71-80. doi:
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