Observation and prediction for the heat equation, III

Abstract

Dirichlet and Neumann data suffices. The pair (p), 9) cannot be specified arbitrarily, but we adopt the viewpoint that, in observation of an ongoing process, any consistency conditions are automatically satisfied; thus, we may assume that the observed pair (p), #) lies in the admissible manifold& and the existence of a solution to the triple (l)-(3), is not at issue. We are concerned here with the well-posedness of the observation/prediction problem; i.e., to show that the map: (v, $) t+ uT is well defined and continuous, using