Solving the Transmission Problem for Open Wave-Guides, II Outgoing Estimates

Autor:	Epstein, Charles L.
Rok vydání:	2023
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Mathematics - Numerical Analysis 35C15 35Q60 65M80 65R20
Druh dokumentu:	Working Paper
Popis:	The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution of the physical problem to a transmission problem rephrased as a system of integral equations on the common perpendicular line. In this part we show that solutions of the integral equations introduced in Part I have asymptotic expansions, if the data allows it. Using these expansions we show that the solutions to the PDE found in each half space satisfy appropriate outgoing radiation conditions. In Part III we show that these conditions imply uniqueness of the solution to the PDE as well as uniqueness for our system of integral equations. Comment: This article contains a completely revised portion of the original version of arXiv:2302.04353
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.05816 Zobrazit plný text záznamu View this record from Arxiv