Inverse boundary value problems for diffusion-wave equation with generalized functions in right-hand sides - Lopushansky, A.O.; Lopushanska, H.P. (Carpathian Mathematical Publications, 2014)
We prove the unique solvability of the problem on determination of the solution $u(x,t)$ of the first boundary value problem for equation $$u^{(β)}_t-a(t)Δ u=F_0(x)· g(t), \;\;\; (x,t) \in (0,l)× (0,T],$$ with fractional derivative $u^{(β)}_t$ of the order $β\in (0,2)$, generalized functions in initial conditions, and also determination of unknown continuous coefficient $a(t)>0, \; t\in [0,T]$ (or unknown continuous function $g(t)$) under given the values $(a(t)u_x(·,t),φ_0(·))$ ($(u(·,t),φ_0(·))$, respectively) of according generalized function onto some test function $φ_0(x)$.