On the evolution equation with a dynamic Hardy-type potential

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

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

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.

原文英語
頁(從 - 到)2141-2165
頁數25
期刊Journal of Evolution Equations
21
發行號2
DOIs
出版狀態已發佈 - 2021 六月

ASJC Scopus subject areas

  • 數學(雜項)

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