Stability for parameter estimation in two point boundary value problems.

In recent years, the use of mathematical models not only in physical or technical sciences, but also for processes in the life sciences like physiology has become a general practice. Often the process of interest can be described by a differential equation the structure of which is determined by general principles, however, the numerical values of certain parameters are unknown [4], [9]. The parameter estimation problem consists of determining these unknown parameters from known observations (data) of the process that is being modelled. In recent years there were many contributions devoted to the numerical aspects of parameter estimation problems (see [3]-[5], [7], [9], [11]-[13] and the references given there, et al.) and to the problem of parameter identifiability; i.e. the injectivity of the map from the parameters to the observations. Furthermore it is wellknown that the parameter-to-observation map is often not continuously invertible and, more generally, the Solutions of parameter estimation problems in their outputleast-squares formulation do not depend continuously on the observations. However, beyond this general observation that such inverse problems are often illposed, this question received comparatively little attention. The main goal of our paper is to study these stability problems.