Recovery of multiple coefficients in a reaction-diffusion equation

Abstract

This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a later time $T$. We show both uniqueness results and the convergence of an iteration scheme designed to recover these coefficients. We also allow a more general setting, in particular when the usual time derivative is replaced by one of fractional order and when the potential term is coupled with a known nonlinearity $f$ of the form $q(x)f(u)$.