On an Integral Equation with Concave Nonlinearity
A nonlinear integral equation on the semi-axis with a special substochastic kernel is studied. Such equations are encountered in the kinetic theory of gases when studying the nonlinear integro-differential Boltzmann equation within the framework of the nonlinear modified Bhatnagar-Gross-Crook model(...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2024-12-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1510 |
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| author | Kh.A. Khachatryan H.S. Petrosyan |
| author_facet | Kh.A. Khachatryan H.S. Petrosyan |
| author_sort | Kh.A. Khachatryan |
| collection | DOAJ |
| description | A nonlinear integral equation on the semi-axis with a special substochastic kernel is studied. Such equations are encountered in the kinetic theory of gases when studying the nonlinear integro-differential Boltzmann equation within the framework of the nonlinear modified Bhatnagar-Gross-Crook model(BGC). Under certain restrictions on nonlinearity, it is possible to construct a positive continuous and bounded solution to this equation. Moreover, the uniqueness of the solution in the class of upper bounded on half-line functions having a positive infimum. It is also proved that the corresponding successive approximations converge uniformly at a rate of some geometric progression to the solution of the indicated equation. Under one additional condition, the asymptotic behavior of the solution at infinity is studied. At the end of the work, specific examples of these equations are given for which all the conditions of the proven facts are automatically met. |
| format | Article |
| id | doaj-art-89eb1fcfaf65472ba36cfe8e2d594f94 |
| institution | Kabale University |
| issn | 1997-7670 2541-8785 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj-art-89eb1fcfaf65472ba36cfe8e2d594f942024-12-07T11:13:22ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852024-12-015016682https://doi.org/10.26516/1997-7670.2024.50.66On an Integral Equation with Concave NonlinearityKh.A. KhachatryanH.S. PetrosyanA nonlinear integral equation on the semi-axis with a special substochastic kernel is studied. Such equations are encountered in the kinetic theory of gases when studying the nonlinear integro-differential Boltzmann equation within the framework of the nonlinear modified Bhatnagar-Gross-Crook model(BGC). Under certain restrictions on nonlinearity, it is possible to construct a positive continuous and bounded solution to this equation. Moreover, the uniqueness of the solution in the class of upper bounded on half-line functions having a positive infimum. It is also proved that the corresponding successive approximations converge uniformly at a rate of some geometric progression to the solution of the indicated equation. Under one additional condition, the asymptotic behavior of the solution at infinity is studied. At the end of the work, specific examples of these equations are given for which all the conditions of the proven facts are automatically met.https://mathizv.isu.ru/en/article/file?id=1510concavityiterationsmonotonicityconvergenceasymptotics |
| spellingShingle | Kh.A. Khachatryan H.S. Petrosyan On an Integral Equation with Concave Nonlinearity Известия Иркутского государственного университета: Серия "Математика" concavity iterations monotonicity convergence asymptotics |
| title | On an Integral Equation with Concave Nonlinearity |
| title_full | On an Integral Equation with Concave Nonlinearity |
| title_fullStr | On an Integral Equation with Concave Nonlinearity |
| title_full_unstemmed | On an Integral Equation with Concave Nonlinearity |
| title_short | On an Integral Equation with Concave Nonlinearity |
| title_sort | on an integral equation with concave nonlinearity |
| topic | concavity iterations monotonicity convergence asymptotics |
| url | https://mathizv.isu.ru/en/article/file?id=1510 |
| work_keys_str_mv | AT khakhachatryan onanintegralequationwithconcavenonlinearity AT hspetrosyan onanintegralequationwithconcavenonlinearity |