Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity

In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the as...

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Autores principales:	Kalimbetov Burkhan T., Tuychiev Olim D.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	singularly perturbed integro-partial differential equation regularization of an integral space of non-resonant solutions iterative problems solvability of iterative problems 35f10 35r09 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9533e1acb7d44946a770b1f893a1165a
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spelling	oai:doaj.org-article:9533e1acb7d44946a770b1f893a1165a2021-12-05T14:10:52ZAsymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity2391-545510.1515/math-2021-0021https://doaj.org/article/9533e1acb7d44946a770b1f893a1165a2021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0021https://doaj.org/toc/2391-5455In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.Kalimbetov Burkhan T.Tuychiev Olim D.De Gruyterarticlesingularly perturbedintegro-partial differential equationregularization of an integralspace of non-resonant solutionsiterative problemssolvability of iterative problems35f1035r09MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 244-258 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	singularly perturbed integro-partial differential equation regularization of an integral space of non-resonant solutions iterative problems solvability of iterative problems 35f10 35r09 Mathematics QA1-939
spellingShingle	singularly perturbed integro-partial differential equation regularization of an integral space of non-resonant solutions iterative problems solvability of iterative problems 35f10 35r09 Mathematics QA1-939 Kalimbetov Burkhan T. Tuychiev Olim D. Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
description	In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.
format	article
author	Kalimbetov Burkhan T. Tuychiev Olim D.
author_facet	Kalimbetov Burkhan T. Tuychiev Olim D.
author_sort	Kalimbetov Burkhan T.
title	Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
title_short	Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
title_full	Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
title_fullStr	Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
title_full_unstemmed	Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
title_sort	asymptotic solution of the cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/9533e1acb7d44946a770b1f893a1165a
work_keys_str_mv	AT kalimbetovburkhant asymptoticsolutionofthecauchyproblemforthesingularlyperturbedpartialintegrodifferentialequationwithrapidlyoscillatingcoefficientsandwithrapidlyoscillatingheterogeneity AT tuychievolimd asymptoticsolutionofthecauchyproblemforthesingularlyperturbedpartialintegrodifferentialequationwithrapidlyoscillatingcoefficientsandwithrapidlyoscillatingheterogeneity
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Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity

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