Loading…

When does the heat equation have a solution with a sequence of similar level sets?

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.

Saved in:
Bibliographic Details
Published in:Annali di matematica pura ed applicata 2015-12, Vol.194 (6), p.1595-1605
Main Authors: Kawakami, Tatsuki, Sakaguchi, Shigeru
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-014-0435-1