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A simple explanation is provided to explain why weighted blow up is observedfor weak solutions of certain semilinear heat equations with Hardy potential.The problem we study has a power non-linearity and a forcing term which dependsonly upon the space variable. Local and global nonexistence results areprovided for this problem. In addition, local existence is proved when thegradient term appearing in the Hardy potential is unimodular almost everywhere.Under additional assumption that the forcing term depends on time as well,global existence is also proved. Through these existence results we predict thecritical exponents for the existence of local and global solutions.

Nonexistence results for a semilinear heat equation with Hardy potential on stratified Lie groups