Abstract
There are studied nonlinear mathematical problems of the interaction of electromagnetic flelds with deformable media. The models are based on combi- nation of the Lam and Maxwell systems coupled through so-called seismomagnetic efiect. Several direct and associated with them inverse problems are studied. Then speaking about the inverse problems, electromagnetic and elastic characteristics of a medium are the subject of reconstruction. The values of physical flelds are con- nected through electromagnetoelastic interactions. We consider the processes which are observed when elastic waves propagate in an elastic electroconducting medium. Variations of the seismic and electromagnetic flelds in this case are called electro- magnetoelastic waves. There are described difierent statements of mathematical model of the electromagnetoelastic interactions. Then the theoretical results of the analytical solution are discussed for various nonlinear direct and inverse problems for the equations of electromagnetoelasticity.
Highlights
Investigation of more complex electromagnetoelastic interactions in a continuous medium requires to consider complex models
The aim of this paper is to study some nonlinear direct and inverse problems connected with electromagnetoelastic interactions
As a rule, the following types of electromagnetoelastic interactions are distinguished: a) Interaction based on the electrokinetic effect
Summary
Viatcheslav Priimenko and Mikhail Vishnevskii abstract: There are studied nonlinear mathematical problems of the interaction of electromagnetic fields with deformable media. Variations of seismic and electromagnetic fields arising in this case are called electromagnetoelastic waves. Such waves contain a certain information about electromagnetic and elastic parameters of the medium. In this case, as a rule, the following types of electromagnetoelastic interactions are distinguished: a) Interaction based on the electrokinetic effect. In seismics and seismology the third type of interaction leads to so-called seismomagnetic effect describing interaction of seismic waves with the Earth’s magnetic field This interaction results in induced electromagnetic waves propagating with speeds commensurable with the speeds of seismic waves. Let us substitute these relations into constitutive equations (1.1.3)
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