Direct and inverse dynamic problems for SH-waves in porous media

Direct and inverse dynamic problems for the equation of SH-waves in porous media are considered. A singular solution of the direct dynamic problem is constructed. A system of nonlinear Volterra integral equations of the second kind is obtained for the dynamic inverse problems in question. Theorems of uniqueness and theorems of existence in the small for the considered inverse problems are proved. Also, theorems of continuous dependence of solutions of inverse dynamic problems on input data are proved.