Shape Reconstruction in a Non-linear Problem

In this paper, we are interested in the shape recognition. This work is an attempt of generalization of works done by the second author with collaborators see Ndiaye et al. (Bull Math Anal Appl 4(1):91–103, 2012) . By using shape optimization and shape derivative we propose a method to recognize a part of a bounded domain in which a boundary non-linear parabolic or elliptic problem is satisfied.