Zeros of complex caloric functions and singularities of complex viscous Burgers equation
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We show that the 1d viscous Burgers equation considered for complex valued functions develops finite-time singularities from compactly supported smooth data. By means of the Cole-Hopf transformation, the singularities of the solutions are related to zeros of complex-valued solutions of the heat equation. We prove that such zeros are isolated if they are not present in the initial data.
16 pages
16 pages