An inverse problem for a system of steady-state reaction-diffusion equations on a porous domain using a collage-based approach

We consider an inverse problem for a system of steady-state reaction-diffusions acting on a perforated domain. We establish several results that connect the parameter values for the problem on the perforated domain with the corresponding problem on the related unperforated of solid domain. This opens the possibility of estimating a solution to the inverse problem on the perforated domain by instead working with the easier-to-solve inverse problem on the solid domain. We illustrate the results with an example.