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 differentiation with respect to time the equation is reduced to a composite type equation with an integral summand. We look for a solution to this equation and unknown coefficients in the integral operator. The boundary conditions are supplemented with the overdetermination conditions which are the values of some functionals of a solution (integrals of a solution with weight, the values of a solution at separate points, etc.). We construct a numerical algorithm for solving this inverse problem and present the results of numerical experiments. The algorithm is based on previously obtained theoretical results, where the problem is reduced to some Volterra equation and the convergence of the method of successive approximations is proven. The corresponding operator in this equation is contractive whenever the time interval is sufficiently small. We use the method of successive approximations and the finite element method.

Keywords:

sobolev-type equation, elliptic equation, equation with memory, ; inverse problem, boundary value problem, numerical solution, finite element method.

PP. 38-45.

DOI: 10.14357/20790279190405

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