TY - JOUR AU - G. P. Lopushanskaya AU - A. O. Lopushanskyi AU - V. Rapita PY - 2016/02/25 Y2 - 2024/03/29 TI - Inverse problem in the space of generalized functions JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 68 IS - 2 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1837 AB - 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 theequation 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 giventest function $\varphi_0$ for any $t \in [0, T]$. ER -