# Recovery of multiple coefficients in a reaction-diffusion equation

## TL;DR

This paper addresses the inverse problem of simultaneously recovering spatially-dependent coefficients in a reaction-diffusion equation, demonstrating uniqueness and convergence of an iterative method, including fractional and nonlinear cases.

## Contribution

It introduces a novel iterative scheme for recovering multiple coefficients in reaction-diffusion equations, extending to fractional derivatives and nonlinear potentials.

## Key findings

- Proves uniqueness of coefficient recovery under given conditions.
- Establishes convergence of the proposed iterative scheme.
- Handles fractional derivatives and nonlinear potential terms.

## 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 $q(x)f(u)$.