The Boundary Value Problem for a Static 2D Klein--Gordon Equation in the Infinite Strip and in the Half-Plane
Dmitry Muravey
TL;DR
This paper derives explicit Green function formulas for a static 2D Klein-Gordon equation in infinite strip and half-plane domains, providing foundational solutions with proofs of uniqueness and existence.
Contribution
It introduces explicit formulas for the Green function of the Klein-Gordon equation in these domains, advancing analytical solution methods.
Findings
Explicit Green function formulas derived for the domains.
Proofs of uniqueness and existence of solutions.
Formulas expressed in elementary and special functions.
Abstract
We provide explicit formulas for the Green function of an elliptic PDE in the infinite strip and the half-plane. They are expressed in elementary and special functions. Proofs of uniqueness and existence are also given.
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Taxonomy
TopicsNumerical methods for differential equations · Stability and Controllability of Differential Equations · Advanced Mathematical Physics Problems