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Effect of a Gradient Term on the Solvability of the Heat Equation with a Supercritical Reaction with Respect to the Hardy Potential

Abstract In this paper we consider the following nonlinear parabolic problem where Ω ⊂ ℝN, N > 2, is a bounded domain with 0 ∈ Ω and 1 < p < 3. The main goal of this work is to analyze the influence of the gradient term in order to obtain the existence of a positive solution for the largest class of data ( f, u0) and for all λ > 0.