Inverse Problems for Mathematical Models of Quasistationary Electromagnetic Waves in Anisotropic Nonmetallic Media with Dispersion

S. G. Pyatkov; S. N. Shergin

doi:10.14529/mmp180105

Authors

S. G. Pyatkov Ugra State University
S. N. Shergin South Ural State University

DOI:

https://doi.org/10.14529/mmp180105

Keywords:

Sobolev-type equation, equation with memory, elliptic equation, inverse problem, boundary value problem

Abstract

We consider inverse problems of evolution type for mathematical models of quasistationary electromagnetic waves. It is assumed in the model that the wave length is small as compared with space inhomogeneities. In this case the electric and magnetic potential satisfy elliptic equations of second order in the space variables comprising integral summands of convolution type in time. After dierentiation with respect to time the equation is reduced to a composite type equation with an integral summand. The boundary conditions are supplemented with the overdetermination conditions which are a collection of functionals of a solution (integrals of a solution with weight, the values of a solution at separate points, etc.). The unknowns are a solution to the equation and unknown coecients in the integral operator. Global (in time) existence and uniqueness theorems of this problem and stability estimates are established.

Author Biographies

S. G. Pyatkov, Ugra State University

Doctor of Physico-Mathematical Sciences

S. N. Shergin, South Ural State University

Postgraduate

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