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) (0,l)× (0,T], with fractional derivative u^(β)_t of the order β(0,2), generalized functions in initial conditions, and also determination of unknown continuous coefficient a(t)>0, t[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).