All articles - Acoustics

Subjects of research: the subjects of this study are waves in porous media with complex reology, the mathematical modeling of dynamic processes of propagation of one-dimensional SH-waves, and also the investigation of the obtained in this study direct and inverse problems.
Purpose of research: the purpose of the thesis are the mathematical modeling of dynamic processes of propagation of SH-waves in which mathematical models are constructed, studying the nature of solution, existence and uniqueness of the solution to obtained in this study direct and inverse problems, the development of numerical methods for solving the problems and programm.
Methods of research: we use mathematical modeling methods, the method of characteristics for hyperbolic systems, the method of integral equations, finite difference methods, the conjugate gradient method, and programming technology.
Results obtained and their novelty: the following results are new:
- derived mathematical model of SH-wave propagation in elastic-porous media;
- constructed singular solutions of SH-wave propagation in elastic-porous media;
- a system of nonlinear Volterra integral equations of the second kind for the dynamic inverse problems for SH-waves in elastic-porous media;
- uniqueness theorem and a "in small" existence of a solution of inverse problems considered, as well as the continuous dependence of solutions to inverse dynamic problems on input data;
- developed numerical method and created program for the numerical solution to the direct and inverse problems for SH-wave propagation in the elastic-porous media.
Practical significance: the results can be used in a broad class of studies of various natural and technological processes.
Degree of embed and economic effectivity: the results may form the basis of special courses on the subject of mathematical modeling for senior undergraduate and graduate students.
Field of application: the results can be used in seismology and in the development of oil and gas deposits.