A note on the identifiability of distributed parameters in elliptic equations. (English) Zbl 0644.35092

Chicone, Carmen; Gerlach, Jürgen

SIAM J. Math. Anal. 18, 1378-1384 (1987).

The authors’ abstract: “For u and f given smooth functions on a bounded domain \(\Omega\) we consider solutions of the PDE \(-div(a\nabla u)=f\) for the parameter a. This problem arises in the identification of the flow of groundwater. We say a is identifiable if, for given u and f, a is unique. Our main result shows that a is identifiable on the points in \(\Omega\) which are the closure of the interior of the set of points which stay in \(\Omega\) for all positive time (or negative time) under the flow of the gradient field \(\nabla u\). We also show a is identifiable on \(\Omega\) if the set of critical points of u has nonempty interior and the co-normal derivative of u is specified on \(\partial \Omega\).”

Reviewer: Dang Dinh Ang

MSC:

35R30	Inverse problems for PDEs
76S05	Flows in porous media; filtration; seepage
35J25	Boundary value problems for second-order elliptic equations

Keywords:

parameter; identification; flow of groundwater; critical points; co- normal derivative