KERNEL DETERMINATION PROBLEM FOR ONE PARABOLIC EQUATION WITH MEMORY
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
KERNEL DETERMINATION PROBLEM FOR ONE PARABOLIC EQUATION WITH MEMORY
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| Автор |
Durdiev, D. K.
Nuriddinov, Zh. Z. |
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| Тематика |
INVERSE PROBLEM
RESOLVENT INTEGRAL EQUATION FIXED POINT THEOREM EXISTENCE UNIQUENESS |
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| Описание |
This paper studies the inverse problem of determining a multidimensional kernel function of an integral term which depends on the time variable t and (n-1)-dimensional space variable x'= (x1, ..., xn-1) in the n-dimensional diffusion equation with a time-variable coefficient at the Laplacian of a direct problem solution. Given a known kernel function, a Cauchy problem is investigated as a direct problem. The integral term in the equation has convolution form: the kernel function is multiplied by a solution of the direct problem’s elliptic operator. As an overdetermination condition, the result of the direct question on the hyperplane xn = 0 is used. An inverse question is replaced by an auxiliary one, which is more suitable for further investigation. After that, the last problem is reduced to an equivalent system of Volterra-type integral equations of the second order with respect to unknown functions. Applying the fixed point theorem to this system in Hölder spaces, we prove the main result of the paper, which is a local existence and uniqueness theorem.
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| Дата |
2024-02-14T05:20:46Z
2024-02-14T05:20:46Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Durdiev D. K. KERNEL DETERMINATION PROBLEM FOR ONE PARABOLIC EQUATION WITH MEMORY / D. K. Durdiev, Zh. Z. Nuriddinov. — Text : electronic // Ural Mathematical Journal. — 2023. — Volume 9. — № 2. — P. 86-98.
2414-3952 https://umjuran.ru/index.php/umj/article/view/579 http://elar.urfu.ru/handle/10995/129435 59690653 10.15826/umj.2023.2.007 |
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| Язык |
en
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| Связанные ресурсы |
Ural Mathematical Journal. 2023. Volume 9. № 2
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| Права |
Creative Commons Attribution License
https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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