A spectral approach to ill-posed problems for wave equations (Q931370)

The authors study the ill-posed problem \[ \begin{cases} u_{tt} + Au(t) = 0, \;t/in (0,T) \\ u(0) = 0, \;u(T) = u_{0},\end{cases} \] where \(A\) is a general selfadjoint operator in a Hilbert space. Under some constraints on \(T\), existence, uniqueness, continuous dependence on data and stability are established for a solution to this problem.