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Direct and inverse scattering problems in dispersive media-Green's functions and invariant imbedding techniques

Publiceringsår: 1990
Språk: Engelska
Sidor: 13
Publikation/Tidskrift/Serie: Technical Report LUTEDX/(TEAT-7006)/1-13/(1990)
Dokumenttyp: Rapport
Ytterligare information: Published version: Direct and Inverse Boundary Volue Problems; Eds. R. Kleinman, R. Kress and E. Martensen, Methoden und Verfahren der Mathematischen Physik, Band 37, pp. 105-119, 1991.


Transient electromagnetic wave propagation in a dispersive medium is reviewed.
The medium is assumed to be 1) linear, 2) invariant to time translations,
3) causal, 4) continuous, and 5) isotropic. The constitutive relations
are then uniquelyrepresen ted bya Riemann-Stieltjes integral in the time variable.
The kernel in this convolution is the susceptibilityk ernel. Two explicit
examples of mathematical models of the susceptibilityk ernel are given. The
medium treated in this paper is assumed to varyonlywith depth. In the direct
problem the reflection and transmission data are computed. The inverse scattering
problem is to find the susceptibilityk ernel from known reflexion data.
It is, thus, a problem of finding a function depending on the time variable. In
the spatiallyhomogeneous case the inverse scattering problem is solved from
reflexion data bysolving a Volterra integral equation of the second kind. This
inverse problem is therefore well-posed and easyto solve.



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