Ultraparabolic Equations with Operator Coefficients at the Time Derivatives
The article is devoted to the study of the solvability of boundary value problems for third-order Sobolev-type differential equations of the third order with two time variables (such equations are also called composite-type equations or equations not solved for the derivative). The peculiarities of...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Irkutsk State University
2019-09-01
|
| Series: | Известия Иркутского государственного университета: Серия "Математика" |
| Subjects: | |
| Online Access: | http://mathizv.isu.ru/en/article/file?id=1314 |
| _version_ | 1818231244713885696 |
|---|---|
| author | A.I. Kozhanov |
| author_facet | A.I. Kozhanov |
| author_sort | A.I. Kozhanov |
| collection | DOAJ |
| description | The article is devoted to the study of the solvability of boundary value problems for third-order Sobolev-type differential equations of the third order with two time variables (such equations are also called composite-type equations or equations not solved for the derivative). The peculiarities of the equations under study are, firstly, that the differential operators acting at the time derivatives are not assumed inverse, and, secondly, that the statements of boundary value problems for them are determined by the coefficients of these differential operators. For the problems proposed in the article, we prove existence and uniqueness theorems for regular solutions (solutions having all weak derivatives in the sense of Sobolev involved in the equation). The technique of proving the existence theorems is based on a special regularization of the equations under study, a priori estimates, and passage to the limit. |
| first_indexed | 2024-12-12T10:47:19Z |
| format | Article |
| id | doaj.art-9d1e60cb229049d99848488b965463e1 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-12-12T10:47:19Z |
| publishDate | 2019-09-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-9d1e60cb229049d99848488b965463e12022-12-22T00:26:52ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852019-09-01291120137https://doi.org/10.26516/1997-7670.2019.29.120Ultraparabolic Equations with Operator Coefficients at the Time DerivativesA.I. KozhanovThe article is devoted to the study of the solvability of boundary value problems for third-order Sobolev-type differential equations of the third order with two time variables (such equations are also called composite-type equations or equations not solved for the derivative). The peculiarities of the equations under study are, firstly, that the differential operators acting at the time derivatives are not assumed inverse, and, secondly, that the statements of boundary value problems for them are determined by the coefficients of these differential operators. For the problems proposed in the article, we prove existence and uniqueness theorems for regular solutions (solutions having all weak derivatives in the sense of Sobolev involved in the equation). The technique of proving the existence theorems is based on a special regularization of the equations under study, a priori estimates, and passage to the limit.http://mathizv.isu.ru/en/article/file?id=1314ultraparabolic equationsirreversible operator coefficientsboundary problemsregular solutionsexistenceuniqueness |
| spellingShingle | A.I. Kozhanov Ultraparabolic Equations with Operator Coefficients at the Time Derivatives Известия Иркутского государственного университета: Серия "Математика" ultraparabolic equations irreversible operator coefficients boundary problems regular solutions existence uniqueness |
| title | Ultraparabolic Equations with Operator Coefficients at the Time Derivatives |
| title_full | Ultraparabolic Equations with Operator Coefficients at the Time Derivatives |
| title_fullStr | Ultraparabolic Equations with Operator Coefficients at the Time Derivatives |
| title_full_unstemmed | Ultraparabolic Equations with Operator Coefficients at the Time Derivatives |
| title_short | Ultraparabolic Equations with Operator Coefficients at the Time Derivatives |
| title_sort | ultraparabolic equations with operator coefficients at the time derivatives |
| topic | ultraparabolic equations irreversible operator coefficients boundary problems regular solutions existence uniqueness |
| url | http://mathizv.isu.ru/en/article/file?id=1314 |
| work_keys_str_mv | AT aikozhanov ultraparabolicequationswithoperatorcoefficientsatthetimederivatives |