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Linearized Inverse Dynamic Problem for the Telegraph
Derivation of a Nonlinear Differential Equation for
Inverse Heat Conduction Problems with Continuously
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absolutely integrable functions Akad analytic function belong boundary conditions CAUCHY data chapter consider const construct continuous function corresponding Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution equation 11 exists family of curves following theorem function u(r function v(p,a fundamental solution given grals GREEN'S function half-plane half-space HOLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic problem inversion formula kernel linearized inverse problem mean values multidimensional inverse problems Nauk SSSR obtain one-dimensional operator L defined parameters potential theory problem for equation problem of determining Prom relations right-hand side satisfies a HOLDER second kind sense of HADAMARD solution to equation space STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family uk(r unique solution uniqueness theorem unit circle unknown function values over spheres variables VOLTERRA equation