One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain

We prove the theorems on the existence and unique determination of a pair of functions: a(t) >0, t ∈ [0,T], and the solution u(x, t) of the first boundary-value problem for the equation Dtβu−atuxx=F0xt,xt∈0l×0T,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{array}{ll}{D}_t^{\beta }u-a(t){u}_{xx}={F}_0\left(x,t\right),\hfill & \left(x,t\right)\in \left(0,l\right)\times \left(0,T\right],\hfill \end{array} $$\end{document}