Inverse Problems · 2001 · 28 citations · 4 references
Natural SciencesMathematicsDynamical SystemsFinite Element AnalysisSystems ModelingBoundary ConditionsBoundary-value ProblemsControl TheoryInverse DynamicsInverse Problems In MechanicsPartial Differential EquationsBoundary Conditions In DynamicsInverse Boundary-value ProblemsInverse Problems In Partial Differential EquationsNeumann Boundary ConditionsParabolic Boundary-value ProblemsRiemannian MetricSystem Theory
An abstract version of the BC method is proposed as a chapter of the linear system theory dealing with dynamical systems with boundary control (DSBCs). A characterization of the response operator of DSBCs is given; a set of models (realizations) of DSBCs determined by the response operator is presented. As an application, a conditional existence theorem characterizing the dynamical Dirichlet-to-Neumann map of the Riemannian manifold is obtained. An abstract analogue of the Gelfand-Levitan-Krein-Marchenko equations is derived.
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