On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem
The author considers the initial/boundary value problem for the wave equation in a bounded domain \(\Omega\subset\mathbb{R}^r\) with a source term of the kind \[ \lambda(t)f(x),\quad \lambda\in C^1[0, T],\quad \lambda(0)\neq 0,\quad f\in L^2(\Omega). \] He studies the inverse problem of determining \(f\) from Neumann boundary data on \(\partial\Omega\) and investigates questions of existence, uniqueness, stability, and stable reconstruction using Tikhonov's regularization.
scientific article; zbMATH DE number 1062469