On singular integral equations with variable limits of integration
The wide range of problems of mathematical physics is reduced to a special Volterra integral equation of the second kind or to integral equations with variable limits of integration. Among such problems we can include: boundary value problems for spectrally loaded differential equations [1-4], inve...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2019-03-01
|
| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/244 |
| _version_ | 1827395641768148992 |
|---|---|
| author | D.M. Akhmanova K.E. Kervenev A.M. Baltabayeva |
| author_facet | D.M. Akhmanova K.E. Kervenev A.M. Baltabayeva |
| author_sort | D.M. Akhmanova |
| collection | DOAJ |
| description |
The wide range of problems of mathematical physics is reduced to a special Volterra integral equation of the second kind or to integral equations with variable limits of integration. Among such problems we can include: boundary value problems for spectrally loaded differential equations [1-4], inverse problems [5, 6], nonlocal problems [7], boundary value problems for domains with moving boundaries as the domain degenerates at the time [8, 9] and others. In the study of integral equations with a variable lower limit of integration, the operational method can not be used directly, since in this case the convolution theorem is not applicable. However, the Laplace transform can be used to study this kind of integral equation by applying the method of model solutions.
|
| first_indexed | 2024-03-08T18:37:44Z |
| format | Article |
| id | doaj.art-1372261d38ae4537b18f6eed52a18b03 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:37:44Z |
| publishDate | 2019-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-1372261d38ae4537b18f6eed52a18b032023-12-29T10:21:02ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-03-0193110.31489/2019m1/8-18On singular integral equations with variable limits of integrationD.M. AkhmanovaK.E. KervenevA.M. Baltabayeva The wide range of problems of mathematical physics is reduced to a special Volterra integral equation of the second kind or to integral equations with variable limits of integration. Among such problems we can include: boundary value problems for spectrally loaded differential equations [1-4], inverse problems [5, 6], nonlocal problems [7], boundary value problems for domains with moving boundaries as the domain degenerates at the time [8, 9] and others. In the study of integral equations with a variable lower limit of integration, the operational method can not be used directly, since in this case the convolution theorem is not applicable. However, the Laplace transform can be used to study this kind of integral equation by applying the method of model solutions. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/244model solutionintegrals operatorspecterresolventcharacteristic numberseigenfunctions |
| spellingShingle | D.M. Akhmanova K.E. Kervenev A.M. Baltabayeva On singular integral equations with variable limits of integration Қарағанды университетінің хабаршысы. Математика сериясы model solution integrals operator specter resolvent characteristic numbers eigenfunctions |
| title | On singular integral equations with variable limits of integration |
| title_full | On singular integral equations with variable limits of integration |
| title_fullStr | On singular integral equations with variable limits of integration |
| title_full_unstemmed | On singular integral equations with variable limits of integration |
| title_short | On singular integral equations with variable limits of integration |
| title_sort | on singular integral equations with variable limits of integration |
| topic | model solution integrals operator specter resolvent characteristic numbers eigenfunctions |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/244 |
| work_keys_str_mv | AT dmakhmanova onsingularintegralequationswithvariablelimitsofintegration AT kekervenev onsingularintegralequationswithvariablelimitsofintegration AT ambaltabayeva onsingularintegralequationswithvariablelimitsofintegration |