Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity
In the present paper, we consider a multidimensional singularly perturbed problem for an elliptic equation referred to as the stationary reaction-diffusion-advection equation in applications. We formulate basic conditions of the existence of solutions with internal transition layers (contrust struct...
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Yaroslavl State University
2017-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/424 |
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| author | Marina A. Davydova Nikolay N. Nefedov |
| author_facet | Marina A. Davydova Nikolay N. Nefedov |
| author_sort | Marina A. Davydova |
| collection | DOAJ |
| description | In the present paper, we consider a multidimensional singularly perturbed problem for an elliptic equation referred to as the stationary reaction-diffusion-advection equation in applications. We formulate basic conditions of the existence of solutions with internal transition layers (contrust structures), and we construct an asymptotic approximation of an arbitrary-order accuracy to such solutions. We use a more efficient method for localizing the transition surface, which permits one to develop our approach to a more complicated case of balanced advection and reaction (the so-called critical case). To justify the constructed asymptotics, we use and develop, to this class of problems, an asymptotic method of differential inequalities, which also permits one to prove the Lyapunov stability of such solutions, as stationary solutions of the corresponding parabolic problems. |
| format | Article |
| id | doaj-art-b44cd7c5947d4c86989afe740059efda |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2017-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-b44cd7c5947d4c86989afe740059efda2025-08-20T03:37:44ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-02-01241313810.18255/1818-1015-2017-1-31-38351Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced NonlinearityMarina A. Davydova0Nikolay N. Nefedov1Lomonosov Moscow State UniversityLomonosov Moscow State UniversityIn the present paper, we consider a multidimensional singularly perturbed problem for an elliptic equation referred to as the stationary reaction-diffusion-advection equation in applications. We formulate basic conditions of the existence of solutions with internal transition layers (contrust structures), and we construct an asymptotic approximation of an arbitrary-order accuracy to such solutions. We use a more efficient method for localizing the transition surface, which permits one to develop our approach to a more complicated case of balanced advection and reaction (the so-called critical case). To justify the constructed asymptotics, we use and develop, to this class of problems, an asymptotic method of differential inequalities, which also permits one to prove the Lyapunov stability of such solutions, as stationary solutions of the corresponding parabolic problems.https://www.mais-journal.ru/jour/article/view/424problems of the reaction-diffusion-advection typesolutions with internal layerscontrust structures |
| spellingShingle | Marina A. Davydova Nikolay N. Nefedov Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity Моделирование и анализ информационных систем problems of the reaction-diffusion-advection type solutions with internal layers contrust structures |
| title | Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity |
| title_full | Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity |
| title_fullStr | Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity |
| title_full_unstemmed | Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity |
| title_short | Existence and Stability of the Solutions with Internal Layers in Multidimensional Problems of the Reaction-Diffusion-Advection Type with Balanced Nonlinearity |
| title_sort | existence and stability of the solutions with internal layers in multidimensional problems of the reaction diffusion advection type with balanced nonlinearity |
| topic | problems of the reaction-diffusion-advection type solutions with internal layers contrust structures |
| url | https://www.mais-journal.ru/jour/article/view/424 |
| work_keys_str_mv | AT marinaadavydova existenceandstabilityofthesolutionswithinternallayersinmultidimensionalproblemsofthereactiondiffusionadvectiontypewithbalancednonlinearity AT nikolaynnefedov existenceandstabilityofthesolutionswithinternallayersinmultidimensionalproblemsofthereactiondiffusionadvectiontypewithbalancednonlinearity |