Parabolic equations with exponential nonlinearity and measure data

Let Ω be a bounded domain in RN and T>0. We study the problem(P±){ut−Δu±g(u)=μin QT:=Ω×(0,T)u=0on ∂Ω×(0,T)u(.,0)=ωin Ω where μ and ω are bounded measures in QT and Ω respectively and g(u)∼ea|u|q with a>0 and q≥1. We provide a sufficient condition in terms of fractional maximal potentials of μ and ω for solving (P±). Moreover, we prove uniqueness for (P+).