Evolution equations of p-Laplace type with absorption or source terms and measure data

Abstract

Let Ω be a bounded domain of ℝN, and Q = Ω × (0, T). We consider problems of the type [Formula: see text] where Δpis the p-Laplacian, μ is a bounded Radon measure, u0∈ L1(Ω), and ±𝒢(u) is an absorption or a source term. In the model case 𝒢(u) = ±|u|q-1u (q > p-1), or 𝒢, has an exponential type. We prove the existence of renormalized solutions for any measure μ in the subcritical case, and give sufficient conditions for existence in the general case, when μ is good in time and satisfies suitable capacitary conditions.