ABSTRACT
Problems of moving boundaries, moving per-meable boundaries, questions of control over wave processes are fundamental physical prob-lems (acc. to V.L.Ginzburg) that exist for a long time from the moment of the wave equation emergence, for over three hundred years. This paper for the first time states a brief, but clear and quite integral disclosure of the author's approaches, and also a physical essence of analytical methods of functions evaluation of wave processes control - the basic processes of the Nature and the natural sciences, character-istic for all objects of the surrounding world without exception and able to occur only in the regions with moving and moving permeable boundaries. Absolutely immovable boundaries do not exist in the nature. Certain examples which are fundamental in theoretical physics of spherical, cylindrical and flat waves, including the waves induced by dilation of the final length cylinder, demonstrate physical, mathematical and engineering lucidity and simplicity (the so-lution comes to a quadratic equation), and, there-fore, the practical value of definition of control function for the predetermined (based on engi-neering requirements) functions of effect. This paper is designated for a wide range of scientific readers, with aim to render to the reader first of all the physical sense of the studied phenome-non, to show the novelty that it has introduced in the development of the corresponding direc-tion, to show that the way of the research (it is more important than the result) has not arisen “out of nothing”, and the gained results are only “a stone which cost him a whole life” (H.Poin-car).