In this paper we study a nonlocal, semilinear, parabolic problem. The existence and uniqueness of a maximal solution is proved for bounded domains, in arbitrary dimensions, using the Schauder fixed-point theorem. In the one-dimensional case, we give a result of positivity and a comparison principle for the integral of the solution. The proofs are based on the decomposition of the solutions in an appropriate spectral basis.
"On some class of problems with nonlocal source and boundary flux." Adv. Differential Equations 6 (9) 1025 - 1048, 2001. https://doi.org/10.57262/ade/1357140403