Variational Approach to Scattering by Unbounded Rough Surfaces with Neumann and Generalized Impedance Boundary Conditions∗

نویسندگان

  • GUANGHUI HU
  • XIAODONG LIU
  • BO ZHANG
چکیده

This paper is concerned with problems of scattering of time-harmonic electromagnetic and acoustic waves from an infinite penetrable medium with a finite height modeled by the Helmholtz equation. On the lower boundary of the rough layer, the Neumann or generalized impedance boundary condition is imposed. The scattered field in the unbounded homogeneous medium is required to satisfy the upward angular-spectrum representation. Using the variational approach, we prove uniqueness and existence of solutions in the standard space of finite energy for inhomogeneous source terms, and in appropriate weighted Sobolev spaces for incident point source waves in Rm (m= 2,3) and incident plane waves in R2. To avoid guided waves, we assume that the penetrable medium satisfies certain non-trapping and geometric conditions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces

This paper is concerned with the variational approach in weighted Sobolev spaces to timeharmonic elastic scattering by two-dimensional unbounded rough surfaces. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the total elastic displacement satisfies either the Dirichlet or impedance boundary condition. We establish uniqueness and ...

متن کامل

Electromagnetic Scattering by Unbounded Rough Surfaces

This paper is concerned with the analysis of the electromagnetic wave scattering in inhomogeneous medium with infinite rough surfaces. Consider a time-harmonic electromagnetic field generated by either a magnetic dipole or an electric dipole incident on an infinite rough surface. Throughout the dielectric permittivity is assumed to have a positive imaginary part which accounts for the energy ab...

متن کامل

Analysis of the scattering by an unbounded rough surface

This paper is concerned with the mathematical analysis of the solution for the wave propagation from the scattering by an unbounded penetrable rough surface. Throughout the wavenumber is assumed to have a nonzero imaginary part which accounts for the energy absorption. The scattering problem is modeled as a boundary value problem governed by the Helmholtz equation with transparent boundary cond...

متن کامل

Existence, Uniqueness, and Variational Methods for Scattering by Unbounded Rough Surfaces

In this paper we study, via variational methods, the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface. The boundary ∂D is assumed to lie within a finite distance of a flat plane and the incident wave is that arising from an inhomogeneous term in the Helmholtz equation whose support lies within some finite distance of the boundary ∂D. Via analysis of an eq...

متن کامل

Asymptotic models for scattering problems from unbounded media with high conductivity

We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014