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.

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.