Green function solution of generalised boundary value problems

We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the boundary value problem of an inhomogeneous partial differentia...

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Bibliographic Details
Published in:arXiv.org 2020-02
Main Authors: Mkrtchian, Vanik E, Henkel, Carsten
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Green's functions
Operators (mathematics)
Partial differential equations
Online Access:Get full text
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Summary:We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the boundary value problem of an inhomogeneous partial differential equation with inhomogeneous, nonlocal, and linear boundary conditions. The construction generally applies for all types of linear partial differential equations and linear boundary conditions.
ISSN:2331-8422
DOI:10.48550/arxiv.2002.12129