In this paper, we consider an initial value problem (IVP) for three dimensional elasticity system in a transversely isotropic inhomogeneous media. We will rewrite the problem in the form of Fourier images by means of Fourier transform method. After some arrangements, the problem is reduced to integral equations in the vector form. Using the properties of the vector integral equation and successive approximations method, an explicit formula for the solution of the IVP in transversely isotropic inhomogeneous media is constructed, and existence and uniqueness of the solution is stated. By a computational example, we illustrate the robustness of the method.
Anisotropic inhomogeneous media, transversely isotropic media, elastodynamic system
"Initial value problem for elastic system in transversely isotropic inhomogeneous media,"
Turkish Journal of Mathematics: Vol. 46:
7, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/11