PARABOLIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND MEASURE DATA PHUOC-TAI NGUYEN

Abstract. Let Ω be a bounded domain in RN and T> 0. We study the problem (0.1) ut −∆u ± g(u) = µ in QT: = Ω × (0, T)u = 0 on ∂Ω × (0, T) u(., 0) = ω in Ω. where µ and ω are bounded Radon measures in QT and Ω respec-tively 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 (0.1)