Inverse problem in the space of generalized functions

  • G. P. Lopushanskaya (Львiв. нац. ун-т, Ряшiв. ун-т, Польща)
  • A. O. Lopushanskyi (Львiв. нац. ун-т, Ряшiв. ун-т, Польща)
  • V. Rapita

Abstract

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 $t \in [0, T]$.
Published
25.02.2016
How to Cite
Lopushanskaya, G. P., A. O. Lopushanskyi, and V. Rapita. “Inverse Problem in the Space of Generalized Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 2, Feb. 2016, pp. 241-53, http://umj.imath.kiev.ua/index.php/umj/article/view/1837.
Section
Research articles