Completeness of products of solutions and some inverse problems for PDE (Q804845)

Building on the completeness of products of solutions to general differential equations, the author solves inverse problems for such equations. For example, if \(\Omega \subset {\mathbb{R}}^ 2\) is a bounded domain, and \(u_ 1,u_ 2\in H^ 2(\Omega \times (0,T))\) are solutions of an initial-boundary value problem for the equation \(\partial^ 2u_ j/\partial t^ 2-\Delta u_ j+a_ ju_ j=0\) on \(\Omega\times (0,T)\), then the coincidence of \(u_ 1\) and \(u_ 2\), and \(\partial u_ 1/\partial t\) and \(\partial u_ 2/\partial t\), on the boundary implies that \(a_ 1=a_ 2\).