Inverse problem in the space of generalized functions
For a linear nonhomogeneous diffusion equation with fractional derivative of order $\beta \in (0, 2)$ with respect to time, we establish a unique solvability of the inverse problem of determination of a pair of functions: the generalized solution u (classical as a function of time) of the first bo...
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| Datum: | 2016 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1837 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | For a linear nonhomogeneous diffusion equation with fractional derivative of order $\beta \in (0, 2)$ with respect to time, we establish a unique solvability of the inverse problem of determination of a pair of functions: the generalized solution u
(classical as a function of time) of the first boundary-value problem for the indicated equation with given generalized functions on the right-hand sides and the unknown (depending on time) continuous coefficient of the minor term of the
equation under the overdetermination condition
$$\bigl( u(\cdot , t), \varphi_0(\cdot ) \bigr) = F(t), t \in [0, T].$$
Here, $F$ is a given continuous function and $(u(\cdot , t), \varphi_0(\cdot ))$ is the value of the unknown generalized function u on a given
test function $\varphi_0$ for any $t \in [0, T]$. |
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