Bulk Green's functions in one-dimensional unsteady problems of elastic diffusion

We consider a one-dimensional unsteady problem of elasticity with diffusion and preset unsteady volumetric disturbances. The mathematical model is based on a local equilibrium model of elastic diffusion. The solution is sought in integral form. The bulk Green's functions are found via Laplace transform and Fourier transform for unbounded medium, sine and cosine transform for semi-bounded medium, Fourier's series for bounded medium.