Nonuniqueness for fractional parabolic equations with sublinear power-type nonlinearity

We show that the parabolic equation u t + ( - Delta) s u = q ( x ) | u | alpha - 1 u posed in a timespace cylinder (0, T ) x R N and coupled with zero initial condition and zero nonlocal Dirichlet condition in (0, T ) x ( R N \ 12), where 12 is a bounded domain, has at least one nontrivial nonnegative finite energy solution provided alpha is an element of (0, 1) and the nonnegative bounded weight function q is separated from zero on an open subset of 12. This fact contrasts with the (super)linear case alpha >= 1 in which the only bounded finite energy solution is identically zero. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.