Regularity of the Parameter-to-State Map of a Parabolic Partial Differential Equation

In this paper, we present results that have been obtained in the DFG-SPP project “Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces and Applications to Nonlinear Inverse Problems”. This project has been concerned with (nonlinear) elliptic and parabolic operator equations on nontrivial domains as well as with related inverse parameter identification problems. In this paper we study analytic properties of the underlying parameter-to-state map, which is motivated by a parabolic model for the embryonal development of drosophila melanogaster.