Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations
For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/5539676 |
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| _version_ | 1832565993808855040 |
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| author | Galina Unguryan |
| author_facet | Galina Unguryan |
| author_sort | Galina Unguryan |
| collection | DOAJ |
| description | For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved. |
| format | Article |
| id | doaj-art-595086df43e5418ea1d23ee9842f3750 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-595086df43e5418ea1d23ee9842f37502025-02-03T01:05:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/55396765539676Modified Cauchy Problem with Impulse Action for Parabolic Shilov EquationsGalina Unguryan0Yu Fed’kovych Chernivtsi National University, 2 Kotsubins’ky Street, 58012 Chernivtsi, UkraineFor parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.http://dx.doi.org/10.1155/2021/5539676 |
| spellingShingle | Galina Unguryan Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations International Journal of Mathematics and Mathematical Sciences |
| title | Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations |
| title_full | Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations |
| title_fullStr | Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations |
| title_full_unstemmed | Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations |
| title_short | Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations |
| title_sort | modified cauchy problem with impulse action for parabolic shilov equations |
| url | http://dx.doi.org/10.1155/2021/5539676 |
| work_keys_str_mv | AT galinaunguryan modifiedcauchyproblemwithimpulseactionforparabolicshilovequations |