Direct and inverse dynamic problems for SH-waves in porous media. (English) Zbl 1170.74027
Summary: We examine direct and inverse dynamic problems for the equation of SH-waves in porous media. A singular solution of the direct dynamic problem is constructed, and a system of nonlinear Volterra integral equations of the second kind is obtained for the dynamic inverse problem in question. Theorems of uniqueness and existence in the small for the considered inverse problems are proved. Also, we prove the continuous dependence of solutions of inverse dynamic problems on input data.
MSC:
| 74J25 | Inverse problems for waves in solid mechanics |
| 74G75 | Inverse problems in equilibrium solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
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