On nonlinear parabolic equations with singular lower order term

Abstract

In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is where is a bounded open subset of ℝ N , N ≥ 2, Q is the cylinder × (0, T), T > 0, Γ the lateral surface × (0, T), q > 0, 𝛾 > 0, and f is non-negative function belonging to some Lebesgue space L m (Q), m ≥ 1 and u 0 ∈ L ∞ ( ) such that Keywords Singular problem • Nonlinear parabolic equations • Lower order term Mathematics Subject Classificationin , ∀ 𝜔 ⊂⊂ 𝛺, ∃ D 𝜔 > 0 ∶ u 0 ≥ D 𝜔 in 𝜔.