Uniqueness conditions and numerical approximation of the solution to M.M. Lavrentiev's integral equation
M.Yu. Kokurin, V.V. Klyuchev
Mary State University, Yoshkar-Ola, Russia
Keywords: wave sensing, hyperbolic equation, coefficient inverse problem, integral equation, uniqueness of solution, quadrature method, conjugate gradient method, parallel calculations
Abstract
M.M. Lavrentiev's linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev's equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallelization of calculations.
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