Hassan Babaei : 1-dimenstional Dirac equation on half-line with Dirichlet boundary conditions

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

Sept. 29, 2025, 4 p.m.

In

636 SEO

Abstract

In this talk, I will present the construction of solutions to the one-dimensional Dirac equation on the half-line with Dirichlet boundary conditions. While the Dirac equation is a four-dimensional system arising in quantum field theory, I will focus on the one- dimensional initial-boundary value problem. The primary analytical tool is the unified transform method (or known as Fokas method), which provides an explicit representation of the solution. To introduce the method, I will first demonstrate it in the context of the heat equation on the half-line. I will then apply it to the Dirac equation to derive explicit solution formulas and analyze the associated boundary behavior at the origin. Furthermore, I will discuss the long-time dynamics of these solutions. If time permits, I will conclude with a discussion of Sobolev-space energy estimates for the solutions, including control of both spatial norms and time-regularity.