Scattering problems

  • Victor Isakov
Part of the Applied Mathematical Sciences book series (AMS, volume 127)


The stationary incoming wave u of frequency k is a solution to the perturbed Helmholtz equation (scattering by medium)
$$ Au - {k^2}u = 0in{\mathbb{R}^3} $$
(A is the elliptic operator − div(a ∇) + b · ∇ + c with ℜb, div b = 0, and ℑc ≤ 0, which coincides with the Laplace operator outside a ball B and which possesses the uniqueness of continuation property) or to the Helmholtz equation (scattering by an obstacle)
$$ \Delta u + {k^2}u = 0\;in\;{D_e} = {\mathbb{R}^3}\backslash \bar D $$
with the Dirichlet boundary data
$$ u = 0\;{\text{on}}\;\partial D\;({\text{soft}}\;{\text{obstacle}}\;D). $$
o the Neumann boundary data
$$ {\partial _v}u = 0\;{\text{on}}\;\partial D\;({\text{hard}}\;{\text{obstacle}}\;D). $$


Dirichlet Problem Radiation Condition Helmholtz Equation Inverse Scattering Double Layer Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Victor Isakov
    • 1
  1. 1.Department of Mathematics and StatisticsThe Wichita State UniversityWichitaUSA

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