Fractional heat equations with subcritical absorption having a measure as initial data

We study existence and uniqueness of weak solutions to (F) ∂tu+(−Δ)αu+h(t,u)=0∂tu+(−Δ)αu+h(t,u)=0 in (0,∞)×RN(0,∞)×RN, with initial condition u(0,⋅)=νu(0,⋅)=ν in RNRN, where N≥2N≥2, the operator (−Δ)α(−Δ)α is the fractional Laplacian with α∈(0,1)α∈(0,1), νν is a bounded Radon measure and h:(0,∞)×R→Rh:(0,∞)×R→R is a continuous function satisfying a subcritical integrability condition.In particular, if h(t,u)=tβuph(t,u)=tβup with β>−1β>−1 and 0