Asymptotic profiles of zero points of solutions to the heat equation

Abstract

In this paper, we analyze the asymptotic profiles of zero points with respect to the spatial variable of the solutions to the heat equation in one-dimensional space. By giving suitable conditions of the initial data, we prove the existence of a zero point such that the asymptotic behavior is O(t) as t → +∞ and its coefficient is characterized by a zero point of the bilateral Laplace transform of the initial data. Furthermore, we reveal the second and third-order asymptotic profiles of the zero point.