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Title: The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels

Abstract

The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.

Authors:
;  [1]
  1. National Research University "Moscow Power Engineering Institute", Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22317926
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 204; Journal Issue: 7; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BIBLIOGRAPHIES; INTEGRO-DIFFERENTIAL EQUATIONS; KERNELS; MATHEMATICAL SOLUTIONS; SINGULARITY; SPECTRA

Citation Formats

Bobodzhanov, A A, and Safonov, V F. The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels. United States: N. p., 2013. Web. doi:10.1070/SM2013V204N07ABEH004327.
Bobodzhanov, A A, & Safonov, V F. The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels. United States. https://doi.org/10.1070/SM2013V204N07ABEH004327
Bobodzhanov, A A, and Safonov, V F. 2013. "The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels". United States. https://doi.org/10.1070/SM2013V204N07ABEH004327.
@article{osti_22317926,
title = {The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels},
author = {Bobodzhanov, A A and Safonov, V F},
abstractNote = {The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.},
doi = {10.1070/SM2013V204N07ABEH004327},
url = {https://www.osti.gov/biblio/22317926}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 7,
volume = 204,
place = {United States},
year = {Wed Jul 31 00:00:00 EDT 2013},
month = {Wed Jul 31 00:00:00 EDT 2013}
}