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
LopushanskayaG. P., LopushanskyiA. O., and RapitaV. “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