Parabolic equations with exponential nonlinearity and measure data

الأصل · EN

Let Ω be a bounded domain in Rⁿ and T>0. We study the problem equation (P){ arraylll uₜ - Δu ± g(u) &= μ &in Qₜ:=Ω× (0,T) ------, u&=0 &on ∂ Ω× (0,T) ----, u(.,0) &=ω&in Ω. array. equation where μ and ω are bounded Radon 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).