Zeros of complex caloric functions and singularities of complex viscous Burgers equation

Details Zeros of complex caloric functions and singularities of complex viscous Burgers equation Zeros of complex caloric functions and singularities of complex viscous Burgers equation

2006-12-18

arxiv.org/abs/math/0612506v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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.

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