The Helmholtz equation on periodic domains in the plane.

Title: The Helmholtz equation on periodic domains in the plane.
Identifier: AAI9325138
identifier: 9325138
Creator: Reller, Austin Fielding.
Contributor: Adviser: Richard Sacksteder
Date: 1993
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: This paper studies the wave equation defined in S{dollar}\sp1{dollar} {dollar}\times{dollar} R. In particular, a technique is developed which can be used to solve boundary value problems of the Helmholtz equation in S{dollar}\sp1\times{lcub}\bf R{rcub}{dollar}. The results are immediately applicable to periodic domains in R{dollar}\sp2{dollar}.;First, a fundamental solution is derived for the Helmholtz equation in S{dollar}\sp1\times{lcub}\bf R{rcub}{dollar}. It is then shown that integral operators may be defined with this fundamental solution or its normal derivative as kernel, and that any integral equation method that can be used to solve boundary value problems for the Helmholtz equation in R{dollar}\sp2{dollar} can be used to solve boundary value problems for the Helmholtz equation in S{dollar}\sp1\times{lcub}\bf R{rcub}{dollar}.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.