Šíření zvukových vln ve stlačitelných tekutinách

Abstract

In the present Thesis we study problems arising in the mathematical theory of propagation of the acoustic waves in compressible uids. In particular, we are interested in problems posed on unbounded or very large spatial domains, where the dispersive phenomena play an important role, and where the local energy of the acoustic waves is likely to decay to zero. We occupy ourselves with problems of small Mach numbers. The latter property is crucial in the study of the incompressible limits, where it provides a rigorous justi cation of \acoustic ltering" amply used in numerical implementations, see [6]. We derive the equation describing the motion of acoustic waves in compressible uids and explore spectral properties of related linear operator. We search situations when its point spectrum is empty, because then we can prove, in the sense of the RAGE Theorem from [7], resp. [1], a decay of the local energy of the acoustic waves as Mach number tends to zero.