ABSTRACT
Medium movement as a whole—movement of medium parameters, movement of a medium boundary together with movement of a medium or without it—leads to various non-stationary phenomena. Apart from the classical uniform movement of a medium or its boundaries, other forms of movement are of interest [1, 2]. Rotational movement has been investigated most often. It leads to the scattering [3–9] and amplification [10, 11] of electromagnetic waves and to the appearance of peculiar ponderomotive effects [12, 13]. The modulation and spectral transformation of electromagnetic waves being reflected from vibrating surfaces have also been investigated [14–17]. Nevertheless, uniform movement is also interesting as, in addition to some fundamental problems, a whole series of new problems is concerned with a complex form of moving boundaries [2, 18] or with the radiation of sources crossing through a moving complex boundary [19, 20]. 278The problem of “paradoxes” of moving boundaries [21–23] is particularly interesting; these paradoxes occur because of a discrepancy in the number of secondary waves and the number of boundary conditions. Abandoning a sharp boundary idealization, and considering a structure with transition layer boundary, is proposed in [21] to resolve these paradoxes. However, it will be shown in this chapter that the Volterra integral equation approach allows these “paradoxes” to be resolved directly.
