Recovery of multiple coefficients in a reaction-diffusion equation

Barbara Kaltenbacher; William Rundell

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arXiv · 1905.12232

Recovery of multiple coefficients in a reaction-diffusion equation

Barbara Kaltenbacher·William Rundell

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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 $q(x)f(u)$.

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Barbara Kaltenbacher, William Rundell. 2019-05-29. Recovery of multiple coefficients in a reaction-diffusion equation. https://arxiv.org/abs/1905.12232

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