One Inverse Problem for the Diffusion-Wave Equation in Bounded Domain - Lopushanskaya, G. P.; Lopushanskyi, A. O. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
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 arrayllD_t^β u-a(t)u_xx=F_0(x,t),& (x,t)(0,l)× (0,T],array with regularized derivative D t β u of the fractional order β ∈ (0, 2) under the additional condition a(t)u x (0, t) = F(t), t ∈ [0,T].