On the construction of solutions for the parabolic Dirac operator and equivalent systems

Abstract

In this manuscript, we characterize the kernel of the parabolic Dirac operator in an explicit way. More precisely, we will show that the members of this kernel equivalently satisfy a generalized div‐curl system. Furthermore, it will be established that it is sufficient to know four scalar solutions of the heat equation to construct explicitly a ‐valued function with 16 components belonging to the kernel of the parabolic Dirac operator. Some additional inherited properties of the heat equation are derived in this work along with concrete examples.