Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/39323
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Gishlarkaev, Vakha I. | - |
dc.date.accessioned | 2023-03-14T19:14:46Z | - |
dc.date.available | 2023-03-14T19:14:46Z | - |
dc.date.issued | 2023-03 | - |
dc.identifier.citation | Gishlarkaev V. I. Fourier transform method for partial differential equations. Part 2. Existence and uniqueness of solutions to the Cauchy problem for linear equations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 21–35. https://doi.org/10.21638/spbu01.2023.103 (In Russian) | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2023.103 | - |
dc.identifier.uri | http://hdl.handle.net/11701/39323 | - |
dc.description.abstract | The article proposes a method for analyzing the Cauchy problem for a wide class of evolutionary linear partial differential equations with variable coefficients. By applying the (inverse) Fourier transform, the original equation is reduced to an integro-differential equation, which can be considered as an ordinary differential equation in the corresponding Banach space. The selection of this space is carried out in such a way that the principle of contraction mappings can be used. To carry out the corresponding estimates for the operators generated by the transformed equation, we impose the conditions of finiteness in the space variable for the inverse Fourier transform of the coefficients, and the spaces of the coefficients of the original equation are determined from the Paley-Wiener Fourier transform theorems. In this case, the apparatus of the theory of the Bochner integral in pseudo-normed spaces, countably-normed spaces and Sobolev spaces is used. Classes of functions are distinguished in which the existence and uniqueness of solutions are proved. For equations with coefficients with separated variables, exact solutions are obtained in the form of a Fourier transform of finite sums for operator exponentials. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10 (68); Issue 1 | - |
dc.subject | Fourier transform | en_GB |
dc.subject | distributions with compact support | en_GB |
dc.subject | convolution | en_GB |
dc.subject | integrodifferential equations | en_GB |
dc.subject | Paley-Wiener theorem | en_GB |
dc.subject | operator exponential | en_GB |
dc.title | Fourier transform method for partial differential equations. Part 2. Existence and uniqueness of solutions to the Cauchy problem for linear equations | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 1 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
15491-Текст статьи-51842-1-2-20230304.pdf | 326,75 kB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.