Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum
In this paper, we consider a system with rapidly oscillating coefficients, which includes an integral operator with an exponentially varying kernel. The main goal of the work is to develop the algorithm of Lomov's the regularization method for such systems and to identify the influence of the i...
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AIMS Press
2021-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021512?viewType=HTML |
| _version_ | 1818650476403490816 |
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| author | Abdukhafiz Bobodzhanov Burkhan Kalimbetov Valeriy Safonov |
| author_facet | Abdukhafiz Bobodzhanov Burkhan Kalimbetov Valeriy Safonov |
| author_sort | Abdukhafiz Bobodzhanov |
| collection | DOAJ |
| description | In this paper, we consider a system with rapidly oscillating coefficients, which includes an integral operator with an exponentially varying kernel. The main goal of the work is to develop the algorithm of Lomov's the regularization method for such systems and to identify the influence of the integral term on the asymptotics of the solution of the original problem. The case of identical resonance is considered, i.e. the case when an integer linear combination of the eigenvalues of a rapidly oscillating coefficient coincides with the points of the spectrum of the limit operator is identical on the entire considered time interval. In addition, the case of coincidence of the eigenvalue of a rapidly oscillating coefficient with the points of the spectrum of the limit operator is excluded. This case is supposed to be studied in our subsequent works. More complex cases of resonance (for example, point resonance) require a more thorough analysis and are not considered in this paper. |
| first_indexed | 2024-12-17T01:50:49Z |
| format | Article |
| id | doaj.art-91549f91c21c482a8b6f5ba3b4dd1196 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T01:50:49Z |
| publishDate | 2021-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-91549f91c21c482a8b6f5ba3b4dd11962022-12-21T22:08:05ZengAIMS PressAIMS Mathematics2473-69882021-06-01688835885310.3934/math.2021512Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrumAbdukhafiz Bobodzhanov0Burkhan Kalimbetov1Valeriy Safonov21. Department of Higher Mathematics, National Research University, MPEI, Krasnokazarmennaya 14, Moscow, 111250, Russia2. Department of Mathematics, Khoja Ahmet Yasawi International Kazakh-Turkish University, B. Sattarkhanov 29, Turkestan, 161200, Kazakhstan1. Department of Higher Mathematics, National Research University, MPEI, Krasnokazarmennaya 14, Moscow, 111250, RussiaIn this paper, we consider a system with rapidly oscillating coefficients, which includes an integral operator with an exponentially varying kernel. The main goal of the work is to develop the algorithm of Lomov's the regularization method for such systems and to identify the influence of the integral term on the asymptotics of the solution of the original problem. The case of identical resonance is considered, i.e. the case when an integer linear combination of the eigenvalues of a rapidly oscillating coefficient coincides with the points of the spectrum of the limit operator is identical on the entire considered time interval. In addition, the case of coincidence of the eigenvalue of a rapidly oscillating coefficient with the points of the spectrum of the limit operator is excluded. This case is supposed to be studied in our subsequent works. More complex cases of resonance (for example, point resonance) require a more thorough analysis and are not considered in this paper.https://www.aimspress.com/article/doi/10.3934/math.2021512?viewType=HTMLsingularly perturbedintegro-differential equationregularization of an integralspace of non-resonant solutionsiterative problemssolvability of iterative problems |
| spellingShingle | Abdukhafiz Bobodzhanov Burkhan Kalimbetov Valeriy Safonov Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum AIMS Mathematics singularly perturbed integro-differential equation regularization of an integral space of non-resonant solutions iterative problems solvability of iterative problems |
| title | Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| title_full | Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| title_fullStr | Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| title_full_unstemmed | Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| title_short | Asymptotic solutions of singularly perturbed integro-differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| title_sort | asymptotic solutions of singularly perturbed integro differential systems with rapidly oscillating coefficients in the case of a simple spectrum |
| topic | singularly perturbed integro-differential equation regularization of an integral space of non-resonant solutions iterative problems solvability of iterative problems |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021512?viewType=HTML |
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