Inverse problems for mathematical models of quasistationary electromagnetic waves in anisotropic nonmetallic media with dispersion

S. G. Pyatkov ; S. N. Shergin

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 1, pp. 44-59

Résumé

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 differentiation 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 coefficients in the integral operator. Global (in time) existence and uniqueness theorems of this problem and stability estimates are established.

Détail

Keywords: Sobolev-type equation; equation with memory; elliptic equation; inverse problem; boundary value problem.

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