On the evolution equation with a dynamic Hardy-type potential

Jann Long Chern, Gyeongha Hwang*, Jin Takahashi, Eiji Yanagida

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Motivated by the celebrated paper of Baras and Goldstein (Trans Am Math Soc 284:121–139, 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.

Original languageEnglish
Pages (from-to)2141-2165
Number of pages25
JournalJournal of Evolution Equations
Issue number2
Publication statusPublished - 2021 Jun


  • Existence
  • Hardy potential
  • Heat equation
  • Initial value problem
  • Singularity
  • Uniqueness

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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