Regularity of the solutions of the boundary value problems for diffusion-wave equation with generalized functions in right-hand sides - Lopushansky, A.O. (Carpathian Mathematical Publications, 2013)
We prove the unique solvability of the first boundary value problem of equation u^(β)_t-a(t)Δ u=F(x,t), (x,t) (0,l)× (0,T], with Riemann-Liouville fractional derivative u^(β)_t of the order β(0,2), positive smooth coefficient a(t) and generalized functions in right-hand sides. We obtain some sufficient conditions of the regularity of its solution as variable t.