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.
Key words:wave sensing, hyperbolic equation, coefficient inverse problem, integral equation, uniqueness
of solution, quadrature method, conjugate gradient method, parallel calculations.
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