PROPERTIES OF THE SOLUTION TO A WAVE EQUATION GIVEN ON A CIRCLE AND METHODS FOR REGULARIZING INVERSE PROBLEMS
Keywords:
wave equation, inverse problems, boundary control method, regularization, boundary observations, Neumann-to-Dirichlet map, Hadamard stability, convergence rates.Abstract
This paper investigates the analytical properties of solutions to the wave equation defined on a bounded trajectory, focusing specifically on how boundary observations can be utilized to reconstruct internal medium parameters. We examine the forward problem's well-posedness and contrast it with the inherent ill-posedness of the corresponding inverse problem. Furthermore, we discuss advanced mathematical frameworks designed to stabilize parameter recovery under the presence of measurement noise, emphasizing boundary control methodologies and regularized minimization strategies.
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