A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations
Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-107-3/6.pdf |
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| author | U.K. Koilyshov K.A. Beisenbaeva S.D. Zhapparova |
| author_facet | U.K. Koilyshov K.A. Beisenbaeva S.D. Zhapparova |
| author_sort | U.K. Koilyshov |
| collection | DOAJ |
| description | Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients are practically not studied. In this work, in an n-dimensional space, a conjugation problem is considered for a heat equation with discontinuous coefficients which degenerates at the initial moment of time. A fundamental solution to the set problem has been constructed and estimates of its derivatives have been found. With the help of these estimates, in the Sobolev classes, the estimate of the solution to the set problem was obtained. |
| first_indexed | 2024-03-11T23:31:10Z |
| format | Article |
| id | doaj.art-d562d82809c54f87973ed913aa249f0c |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-11T23:31:10Z |
| publishDate | 2022-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-d562d82809c54f87973ed913aa249f0c2023-09-20T10:02:32ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-09-011073596910.31489/2022M3/59-69A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equationsU.K. KoilyshovK.A. BeisenbaevaS.D. Zhapparova Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors. Conjugation problems for time-degenerate equations of the parabolic type with discontinuous coefficients are practically not studied. In this work, in an n-dimensional space, a conjugation problem is considered for a heat equation with discontinuous coefficients which degenerates at the initial moment of time. A fundamental solution to the set problem has been constructed and estimates of its derivatives have been found. With the help of these estimates, in the Sobolev classes, the estimate of the solution to the set problem was obtained.https://mathematics-vestnik.ksu.kz/apart/2022-107-3/6.pdf |
| spellingShingle | U.K. Koilyshov K.A. Beisenbaeva S.D. Zhapparova A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations Қарағанды университетінің хабаршысы. Математика сериясы |
| title | A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations |
| title_full | A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations |
| title_fullStr | A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations |
| title_full_unstemmed | A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations |
| title_short | A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations |
| title_sort | priori estimate of the solution of the cauchy problem in the sobolev classes for discontinuous coefficients of degenerate heat equations |
| url | https://mathematics-vestnik.ksu.kz/apart/2022-107-3/6.pdf |
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