Bitsadze–Samarskii problem for a parabolic system on the plane

详细

The solvability (in classical sense) of the Bitsadze–Samarskii nonlocal initial–boundary value problem for a one-dimensional (in x) second-order parabolic system in a semibounded domain with a nonsmooth lateral boundary is proved by applying the method of boundary integral equations. The only condition imposed on the right-hand side of the nonlocal boundary condition is that it has a continuous derivative of order 1/2 vanishing at t = 0. The smoothness of the solution is studied.