منابع مشابه
Inverse scattering: asymptotic analysis
If an acoustic field is governed by the equation V 2 u + w 2 u + u2al (x)u + V (az(x)Vu) = -S(x-y) in R and U is measured on the surface of the earth, i.e. on the plane x3 = 0 for all positions of the source y and receiver x and for all frequencies, then: (i) we show that the low frequency portion of the data determines a 2 ( x ) while the high frequency portion of the data determines ( a , -a2...
متن کاملDimensions: Inverse Scattering Analysis
Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We report here on our non-perturbative analysis of this phenomenon in the 1+1 dimensional massive Gross-Neveu model, in the large N limit. Our main result is that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. Explicit formulas for the profiles and mass...
متن کاملAnalysis of the Hessian for inverse scattering problems: II. Inverse medium scattering of acoustic waves
We address the inverse problem for scattering of acoustic waves due to an inhomogeneous medium. We derive and analyze the Hessian in both Hölder and Sobolev spaces. Using an integral equation approach based on Newton potential theory and compact embeddings in Hölder and Sobolev spaces, we show that the Hessian can be decomposed into two components, both of which are shown to be compact operator...
متن کاملAnalysis of the Hessian for inverse scattering problems: I. Inverse shape scattering of acoustic waves
We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...
متن کاملAnalysis of the Hessian for Inverse Scattering Problems. Part I: Inverse Shape Scattering of Acoustic Waves
We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 1986
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/2/4/001