Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy

A simultaneous reconstruction of the initial condition and space-dependent reaction coefficient in a multidimensional hyperbolic partial differential equation with interior degeneracy is concern. temporal integral observation utilized to achieve that purpose. The well-posedness, existence, uniqueness inverse problem under consideration are discussed. can be reformulated as least squares minimization Fréchet gradients determined, using adjoint sensitivity problems. Finally, an iterative construction procedure developed by employing conjugate gradient algorithm while invoking discrepancy principle stopping criterion. Some numerical experiments given ensure performance scheme one two dimensions.