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Beschreibung:
We consider a wave equation with point source terms: $$ \left\{\aligned \frac{\partial^2 u}{\partial t^2}(x,t) & = \frac{\partial^2 u}{\partial x^2} (x,t) + \lambda(t)\sum^N_{k=1}\alpha_k\delta(x-x_k), \qquad 0<x< 1, \thinspace 0 0$. \par We prove uniqueness and stabilty in determining point sources in terms of the norm in $H^1(0,T)$ of observations. The uniqueness result requires that $\eta$ is an irrational number and $T \ge 1$, and our stability result further needs a-priori (but reasonable) informations of unknown $\{ x_1, ., x_N \}$. Moreover, we establish two schemes for reconstructing $\{ x_1, ., x_N \}$ which are stable against errors in $L^2(0,T)$.