Half Dirichlet Problems for Parabolic Dirac Equations and Applications

ABSTRACT A parabolic Dirac operator, which is a first order differential operator, was firstly constructed as a square root of the heat operator without involving fractional derivatives. In this article, we study half Dirichlet problems for the parabolic Dirac equations in the unit ball and the upper half space. Further, we introduce connections between half Dirichlet problems for the parabolic Dirac equations and Dirichlet problems for the iterated generalized heat equations.