@article{84f2a3017df84ad4a22def4527fa1c78,

title = "When does the heat equation have a solution with a sequence of similar level sets?",

abstract = "In this paper, we consider an overdetermined Cauchy problem for the heat equation. We prove that if the problem has a non-trivial nonnegative solution with a certain sequence of similar level sets, then the solution must be radially symmetric.",

keywords = "Heat equation, Overdetermined Cauchy problem, Similar level sets",

author = "Tatsuki Kawakami and Shigeru Sakaguchi",

note = "Funding Information: The first and second authors were supported by the Grants-in-Aid for Young Scientists (B) (No. 24740107) and for Challenging Exploratory Research (No. 25610024) from Japan Society for the Promotion of Science, respectively. The authors would like to thank the anonymous referee for his/her some valuable suggestions to improve the presentation and clarity in several points. Publisher Copyright: {\textcopyright} 2014, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = jun,

day = "15",

doi = "10.1007/s10231-014-0435-1",

language = "English",

volume = "194",

pages = "1595--1605",

journal = "Annali di Matematica Pura ed Applicata",

issn = "0373-3114",

publisher = "Springer Verlag",

number = "6",

}