When does the heat equation have a solution with a sequence of similar level sets?
arXiv:1403.6203 · doi:10.1007/s10231-014-0435-1
Abstract
In this paper we consider the overdetermined Cauchy problem for the heat equation. We prove that if the problem has a nontrivial nonnegative solution with a certain sequence of similar level sets, then the solution must be radially symmetric.