@article{aa6beed6242e4bb9b9586c37c34dda93,
title = "On the evolution equation with a dynamic Hardy-type potential",
abstract = "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.",
keywords = "Existence, Hardy potential, Heat equation, Initial value problem, Singularity, Uniqueness",
author = "Chern, {Jann Long} and Gyeongha Hwang and Jin Takahashi and Eiji Yanagida",
note = "Funding Information: The first author was supported in part by Ministry of Science and Technology (MOST) of Taiwan (No. MOST 107-2115-M-008-005-MY3). The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korean government(MSIT) (No. NRF-2018R1C1B5086492). The third author was supported in part by JSPS KAKENHI Early-Career Scientists (No. 19K14567). The fourth author was supported in part by JSPS KAKENHI Grant-in-Aid for Scientific Research (A) (No. 16K13769). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.",
year = "2021",
month = jun,
doi = "10.1007/s00028-021-00675-5",
language = "English",
volume = "21",
pages = "2141--2165",
journal = "Journal of Evolution Equations",
issn = "1424-3199",
publisher = "Birkhauser Verlag Basel",
number = "2",
}