On the regularizing effects of coefficient interactions in singular parabolic problems with a Hardy potential

Abstract

We study a class of parabolic equations involving Hardy-type potentials, singular source terms, and absorption effects. We first establish the existence and uniqueness of finite-energy weak solutions under suitable control conditions on the Hardy potential coefficient, together with appropriate interaction assumptions between the zero-order term and the data. We then prove the existence of bounded finite-energy solutions without imposing any restriction on the Hardy potential coefficient by relying on specific interaction conditions between the zero-order term, the Hardy potential, and the data.