Regularizing effect and decay results for a parabolic problem with repulsive superlinear first order terms

Abstract

We want to analyse both regularizing effect and long, short time decay concerning parabolic Cauchy-Dirichlet problems of the typein Ω.We assume that A(t, x) is a coercive, bounded and measurable matrix, the growth rate q of the gradient term is superlinear but still subnatural, γ > 0, the initial datum u 0 is an unbounded function belonging to a well precise Lebesgue space L σ (Ω) for σ = σ(q, p, N).