Uniqueness of very weak solutions for a fractional filtration equation

We prove existence and uniqueness of distributional, bounded solutions to a fractional filtration equation in R-d. With regards to uniqueness, it was shown even for more general equations in [22] that if two bounded solutions u, w of (1.1) satisfy u - w E L-l (R-d x (0, T)), then u = w. We obtain here that this extra assumption can in fact be removed and establish uniqueness in the class of merely bounded solutions. For nonnegative initial data, we first show that a minimal solution exists and then that any other solution must coincide with it. A similar procedure is carried out for sign-changing solutions. As a consequence, distributional solutions have locally-finite energy. (C) 2020 Elsevier Inc. All rights reserved.