A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation-Reference-Cited by-同舟云学术

A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation

Published:2023-02-28 Issue:5 Volume:31 Page:669-685
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Maréchal Pierre¹,Simo Tao Lee Walter¹,Triki Faouzi²

Affiliation:

1. Institut de Mathématiques , Université Paul Sabatier , 31062 Toulouse , France

2. Laboratoire Jean Kuntzmann , UMR CNRS 5224 , Université Grenoble-Alpes , 700 Avenue Centrale, 38401 Saint-Martin-d’Hères , France

Abstract

Abstract The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2021-0028/pdf

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