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The main purpose of this article is the study of an inverse problem fornonlocal porous medium equations (NPMEs) with a linear absorption term. Moreconcretely, we show that under certain assumptions on the time-independentcoefficients $\rho,q$ and the time-independent kernel $K$ of the nonlocaloperator $L_K$, the (partial) Dirichlet-to-Neumann map uniquely determines thethree quantities $(\rho,K,q)$ in the nonlocal porous medium equation $\rho\partial_tu+L_K(u^m)+qu=0$, where $m>1$. In the first part of this work weadapt the Galerkin method to prove existence and uniqueness of nonnegative,bounded solutions to the homogenoeus NPME with regular initial and exteriorconditions. Additionally, a comparison principle for solutions of the NPME isproved, whenever they can be approximated by sufficiently regular functionslike the one constructed for the homogeneous NPME. These results are then usedin the second part to prove the unique determination of the coefficients$(\rho,K,q)$ in the inverse problem. Finally, we show that the assumptions onthe nonlocal operator $L_K$ in our main theorem are satisfied by the fractionalconductivity operator $\mathcal{L}_{\gamma}$, whose kernel is$\gamma^{1/2}(x)\gamma^{1/2}(y)/|x-y|^{n+2s}$ up to a normalization constant.

Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term