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粗糙曲面上各向异性介质层散射问题的适定性 被引量：2

Well-Posedness of Anisotropic Layers Scattering above Rough Surfaces
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摘要 考虑时谐声波在无界粗糙声软界面上各项异性介质中散射问题的数学模型,先将问题转化为变分形式,验证了双线性形式满足inf-sup条件,通过建立Rellich型恒等式,并应用广义Lax-Milgram定理,证明了变分问题对任意波数都是唯一可解的,同时给出了解的先验估计.所得结果也适合于更一般的介质问题,不再局限于各项同性介质. We considered the mathematical model of scattering prob lem for time harmonic acoustic waves in anisotropic media above an unbounded sou nd soft rough surface.We gave a variational form of the problem and established the inf-sup condition of the sesquilinear form.By means of a Rellich-like id entity and the generalized Lax-Milgram theorem,we proved that the variatio nal problem is uniquely solvable for arbitrary wave number and we also gave a pr iori estimation.These results are available for more general media besides isotropic ones.
作者 栾天 马富明
机构地区 吉林大学数学研究所 北华大学数学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2012年第2期213-218,共6页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10971083)
关键词 散射问题 HELMHOLTZ方程 粗糙曲面 scattering problem Helmholtz equation rough surface
分类号 O29 [理学—应用数学]
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参考文献11

  • 1Chandler-Wilde S N,Monk P.Existence,Uniqueness,and Variational Methods for Scattering by Unbounded RoughSurfaces[J].SIAM J Math Anal,2005,37(2):598-618.
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同被引文献16

  • 1CHEN Xin-fu, Friedman A. Maxwell's Equations in a Periodic Structure [J]. Trans Amer Math Soc, 1991, 323(2): 465-507.
  • 2Friedman A. Mathematics in Industrial Problems [M]. Part 3. Heidelberg: Springer-Verlag, 1990.
  • 3Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory [M]. Berlin: Springer, 1992: 1-199.
  • 4Dobson D, Friedman A. The Time Harmonic Maxwell Equations in a Doubly Periodic Structure [J]. Journal of Mathematical Analysis and Applications, 1992, 166(2) : 507-528.
  • 5BAO Gang, Cowsar L, Masters W. Mathematical Modeling in Optical Science [M]. Philadelphia: Frontiers in Applied Mathematics, 2001.
  • 6BAO Gang. Numerical Analysis of Diffraction by Periodic Structures: TM Polarization [J]. Numer Math, 1996, 75(1) : 1-16.
  • 7BAG Gang, CAO Yan zhao, YANG Hong-tao. Numerical Solution of Diffraction Problems by a Least-Squares Finite Element Method [J]. Math Methods Appl Sci, 2000, 23(12) : 1073-1092.
  • 8BAO Gang, CHEN Zhi ming, WU Hai-jun. Adaptive Finite-Element Method for Diffraction Gratings [J]. J Opt Soc Am A, 2005, 22(6): 1106-1114.
  • 9Deraernaeker A, Babugka I, Bouillard P. Dispersion and Pollution of the FEM Solution for the Helmholtz Equation in One, Two and Three Dimensions [J]. Int J Numer Meth Eng, 1999, 46(4) : 471-499.
  • 10Moiola A, Hiptmair R, Perugia I. Plane Wave Approximation of Homogeneous Helmholtz Solutions [J]. Z Angew Math Phys, 2011, 62(5): 809-837.

引证文献2

二级引证文献7

吉林大学学报（理学版）
2012年 第2期

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