On the Continuous Dependence of the Exterior Dirichlet Problem on the Boundary

Hähner, P.

doi:10.1002/(sici)1099-1476(19970525)20:8<707::aid-mma880>3.0.co;2-l

Math. Meth. Appl. Sci.

1997

DOI: 10.1002/(sici)1099-1476(19970525)20:8<707::aid-mma880>3.0.co;2-l

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On the Continuous Dependence of the Exterior Dirichlet Problem on the Boundary

P. Hähner

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2003

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Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications

Dermenjian

Jalade

2003

Math Methods in App Sciences

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SUMMARYThis paper deals with the behaviour of k-outgoing solutions of − u − k 2 u = f outside a fading soft obstacle. We extend an approach using the so-called Lax-Phillips construction and the well-known properties of the capacity of smooth obstacles. So, classical results are recovered in a straightforward manner. The previous approach enables us to consider the case of obstacles composed of many tiny spheres. Roughly speaking, we prove that the scattering amplitude is approximately the sum of the scattering amplitudes scattered by each isolated sphere, which is an alternative form of the ÿrst Born approximation. As a consequence, two inverse problems are solved.

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Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications

Dermenjian

Jalade

2003

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

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On the Continuous Dependence of the Exterior Dirichlet Problem on the Boundary

Cited by 1 publication

References 9 publications

Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications

Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications

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On the Continuous Dependence of the Exterior Dirichlet Problem on the Boundary

Cited by 1 publication

References 9 publications

Behaviour of (−Δ−k2−i0+)−1 outside fading obstacles, independant scattering hypothesis and applications

Behaviour of (−Δ−k2−i0+)−1 outside fading obstacles, independant scattering hypothesis and applications

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Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications

Behaviour of (−Δ−k²−i0⁺)⁻¹ outside fading obstacles, independant scattering hypothesis and applications