Fourier Transform of Fundamental Solutions for the Motion Equations of Two-component Biot's Media

摘要

Here the two-component medium of M. Biot is considered which contains elastic and water components. To obtain the solutions of motion equations for this medium the Fourier transformations of fundamental solutions for them are constructed. For their definition the divergence method are used. As the fundamental solutions are determined with a precision of solutions of homogeneous system, their generalized Fourier transform determines a class of originals with different asymptotic properties. To highlight the physical fundamental solutions satisfying the radiation conditions (the Green tensor), the regularization of these transforms is performed. Fourier inversion of fundamental solutions depending on the dimension of the space, in which the problem is solved, is discussed.