# Initial boundary value problem for nonlinear Dirac equation of Gross-Neveu type in $1+1$ dimensions

## TL;DR

This paper establishes the global existence and uniqueness of strong solutions for a nonlinear Dirac equation with cubic terms and moving boundary conditions in one spatial and one temporal dimension.

## Contribution

It provides the first rigorous proof of global well-posedness for this class of nonlinear Dirac equations with moving boundaries.

## Key findings

- Proved global existence of solutions.
- Established uniqueness of solutions.
- Handled moving boundary conditions effectively.

## Abstract

This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms and moving boundary. For the initial data with bounded $L^2$ norm and the suitable boundary conditions, the global existence and the uniqueness of the strong solution are proved.