| Abstract: |
| Motivated by the celebrated paper of Baras and Goldstein (Trans Am Math Soc ,1984), we study the heat equation with a dynamic Hardy-type singular potential. In particular, we are
interested in the case where the singular point moves in time. Under appropriate conditions on the potential
and initial value, we show the existence, nonexistence and uniqueness of solutions and obtain a sharp lower
and upper bound near the singular point. Proofs are given by using solutions of the radial heat equation,
some precise estimates for an equivalent integral equation and the comparison principle. |
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