# Inhomogeneous Boundary Value Problem for Hartree Type Equation

## TL;DR

This paper addresses the inhomogeneous boundary value problem for the time-dependent Hartree equation in bounded Lipschitz domains, establishing conditions for global existence of solutions.

## Contribution

It provides the first comprehensive analysis of the inhomogeneous boundary problem for the Hartree equation with a global existence result.

## Key findings

- Proved global existence of solutions under certain conditions.
- Extended the analysis of Hartree equations to inhomogeneous boundary conditions.
- Established mathematical framework for future research in similar boundary value problems.

## Abstract

In this paper, we settle the problem for time-dependent Hartree equation with inhomogeneous boundary condition in a bounded Lipschitz domain in $\mathbb{R}^{N}$. A global existence result is derived.