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Green functions and propagation of waves in strongly inhomogeneous media

Z Haba

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We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of the Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium.


PACS

41.20.Jb Electromagnetic wave propagation; radiowave propagation

02.30.Gp Special functions

02.30.Jr Partial differential equations

MSC

32Wxx Differential operators in several variables

34B27 Green functions

58J05 Elliptic equations on manifolds, general theory (See also 35-XX)

Subjects

Mathematical physics

Accelerators, beams and electromagnetism

Dates

Issue 39 (1 October 2004)

Received 13 May 2004, in final form 17 August 2004

Published 15 September 2004



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