On a multi-dimensional inverse parabolic problem (Q1083621)

In this announcement the author considers an inverse problem for a linear parabolic equation in a bounded domain \(\Omega\) where \(\Omega =(0,1)\times S^ 1:\) \[ u_ t-\Delta u+pu=0\quad in\quad \Omega \times [0,T] \] \[ \partial u/\partial \eta =F\quad in\quad \partial \Omega \times [0,T],\quad u(x,0)=0,\quad x\in \Omega. \] The author proves a uniqueness theorem for the inverse problem associated with the above equation provided p is real analytic and F satisfies suitable conditions. Nice new ideas are presented in the outline of the proof and the main difficulties are due to the need to extend the well-known Gelfand- Levitan's theory to higher dimensions.