Recovery of multiple coefficients in a reaction-diffusion equation
Provides theoretical guarantees for a challenging inverse problem in parabolic PDEs, relevant for applications like parameter identification in physical and biological systems.
The paper addresses the inverse problem of recovering two unknown coefficients (conductivity and potential) in a reaction-diffusion equation from time-T solution data, proving uniqueness and iterative scheme convergence, including fractional derivatives and nonlinear potentials.
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 $q(x)f(u)$.