Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations
The work is aimed to study front solutions of a nonlinear system of parabolic equations in a two-dimensional region. The system can be considered as a mathematical model describing an abrupt change in physical characteristics of spatially heterogeneous media. We consider a system with small paramete...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2018-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/636 |
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| author | Alina A. Melnikova Natalia N. Deryugina |
| author_facet | Alina A. Melnikova Natalia N. Deryugina |
| author_sort | Alina A. Melnikova |
| collection | DOAJ |
| description | The work is aimed to study front solutions of a nonlinear system of parabolic equations in a two-dimensional region. The system can be considered as a mathematical model describing an abrupt change in physical characteristics of spatially heterogeneous media. We consider a system with small parameters raised to the different powers at a differential operator, that represents the difference of typical processes speeds for the system components. The study of the system is conducted by using the contrast structures theory methods, which allowed us to obtain conditions for the existence of front solutions contained in the neighborhood of a closed curve, to determine the front velocity depending on time and coordinate along the front curve, and to obtain the zero-order and the first-order terms of the asymptotic approximation to the solution. The scope of the system includes the description of autowave solutions in the field of ecology, biophysics, combustion physics and chemical kinetics. The approximate solution allows us to choose the model parameters so that the result corresponds to the processes observed, to explain and describe the characteristics of the solutions with sharp gradients, to create models with stable solutions and thereby to simplify the numerical analysis. Note that the numerical experiment for the two-dimensional spatial models requires a considerable amount of processing power and the use of parallel computing techniques and does not allow to effectively analyze and modify the model. In this paper, we obtain the asymptotic approximation that is to be justified, which can be done by the method of differential inequalities. |
| format | Article |
| id | doaj-art-28f6d33990bb44a49278c06a67b2d3b7 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2018-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-28f6d33990bb44a49278c06a67b2d3b72025-08-20T03:37:50ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172018-02-0125111212410.18255/1818-1015-2018-1-112-124461Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic EquationsAlina A. Melnikova0Natalia N. Deryugina1Moscow Lomonosov State UniversityMoscow Lomonosov State UniversityThe work is aimed to study front solutions of a nonlinear system of parabolic equations in a two-dimensional region. The system can be considered as a mathematical model describing an abrupt change in physical characteristics of spatially heterogeneous media. We consider a system with small parameters raised to the different powers at a differential operator, that represents the difference of typical processes speeds for the system components. The study of the system is conducted by using the contrast structures theory methods, which allowed us to obtain conditions for the existence of front solutions contained in the neighborhood of a closed curve, to determine the front velocity depending on time and coordinate along the front curve, and to obtain the zero-order and the first-order terms of the asymptotic approximation to the solution. The scope of the system includes the description of autowave solutions in the field of ecology, biophysics, combustion physics and chemical kinetics. The approximate solution allows us to choose the model parameters so that the result corresponds to the processes observed, to explain and describe the characteristics of the solutions with sharp gradients, to create models with stable solutions and thereby to simplify the numerical analysis. Note that the numerical experiment for the two-dimensional spatial models requires a considerable amount of processing power and the use of parallel computing techniques and does not allow to effectively analyze and modify the model. In this paper, we obtain the asymptotic approximation that is to be justified, which can be done by the method of differential inequalities.https://www.mais-journal.ru/jour/article/view/636singular perturbationsurbo ecosystemautowave solutioninternal transition layerreaction-diffusion system |
| spellingShingle | Alina A. Melnikova Natalia N. Deryugina Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations Моделирование и анализ информационных систем singular perturbations urbo ecosystem autowave solution internal transition layer reaction-diffusion system |
| title | Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations |
| title_full | Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations |
| title_fullStr | Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations |
| title_full_unstemmed | Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations |
| title_short | Periodic Variations of an Autowave Structure in Two-dimensional System of Parabolic Equations |
| title_sort | periodic variations of an autowave structure in two dimensional system of parabolic equations |
| topic | singular perturbations urbo ecosystem autowave solution internal transition layer reaction-diffusion system |
| url | https://www.mais-journal.ru/jour/article/view/636 |
| work_keys_str_mv | AT alinaamelnikova periodicvariationsofanautowavestructureintwodimensionalsystemofparabolicequations AT natalianderyugina periodicvariationsofanautowavestructureintwodimensionalsystemofparabolicequations |