An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

B. Tomas Johansson; Vladimir A. Kozlov

doi:10.1093/imamat/hxn013

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

B. Tomas Johansson, Vladimir A. Kozlov

Research output: Contribution to journal › Article › peer-review

Abstract

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Original language	English
Pages (from-to)	62-73
Number of pages	12
Journal	IMA Journal of Applied Mathematics
Volume	74
Issue number	1
Early online date	3 Jul 2008
DOIs	https://doi.org/10.1093/imamat/hxn013
Publication status	Published - 2009

Keywords

Cauchy problem
Helmholtz equation

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10.1093/imamat/hxn013

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abstract = "Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given. ",

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AU - Kozlov, Vladimir A.

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AB - Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

KW - Cauchy problem

KW - Helmholtz equation

UR - https://academic.oup.com/imamat/article/74/1/62/742691

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DO - 10.1093/imamat/hxn013

M3 - Article

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JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 1

ER -

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

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Keywords

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