IDENTIFIABILITY OF DISTRIBUTED PARAMETERS

This chapter discusses the criteria of identifiability of distributed parameters. It focuses on the equation –div( a ▽ u ) = f on Q , which arises in the study of aquifer flows or petroleum reservoir modeling. The identification problem consists of determination of a from the data u and f . While most of the efforts are directed toward numerical parameter estimation and the development of stable reliable algorithms, the chapter presents a different issue: if u and f are known everywhere in Q and no measurement errors are present, under which conditions is a uniquely determined by the equation –div( a ▽ u ) = f on Q .